Therefore, a linear equation in two variables has infinitely many solutions. Thus, y = 3x + 5 has infinitely many solutions. Hence (iii) is the correct answer.
Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $118,500 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions. What is Richard’s net pay for the week if he earns $1,700?
Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.
First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.
Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.
To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.
Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.
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1. how long is the hall which has a perimeter if 3480 cm and 300cm wide?
2. joe walks across the rotonda and travels 400meters, how many more meters will a car travel around it than the distance the pedestrian walk?
3.father will fence the rectangular yard with a length of 120m and a width of 100m,
how many meters of wire will her use for the fence?
Answer:
(3480 - 600)/2 = 1440cm
Step-by-step explanation:
--------% of 250 =75 and 75% of ------ =300%
Answer:
30%
Step-by-step explanation:
First have to divide 75 by 250 then multiply by 100
75% 0f 225=300%
Brian scored 92, 87 and 88 on three science tests. Write and solve an equation to find the score Brian will need on the fourth science test so that the mean test score is 90.
Answer:
You would need to score a 93% to have an average of 90.
Step-by-step explanation:
Well, to check my work you would need to find the average.
So, 93 + 92 + 88 + 87 = 360. Then you divide by four; 360 / 4 = 90. ^^
what two numbers multiply to be 12 and add to be -11?
Answer:
-12 and 1
Step-by-step explanation:
If you multiply 12 by 1 you get 12, hence if you add -12 and 1 now you will get -11
The two numbers that multiply to be 12 and add to be -11, obtained using the quadratic formula are;
(-11 + √(73))/2, and 24/(-11 + √(73))
(-11 - √(73))/2 and 24/(-11 - √(73))
What is the quadratic formula?The quadratic formula is a formula that can be used to find the solution to a quadratic equation in the form; y = a·x² + b·x + c, where a ≠ 0, and a, b, and c are constant.
The quadratic formula can be presented as follows;
x = \(\frac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}\)
Let x represent one of the numbers,. and let y represent the other number, we get;
x × y = 12...(1)
x + y = -11...(2)
Solving for y in the first equation, we get;
y = 12/x
Substituting the value for y above in equation (2), we get;
x + 12/x = -11
x² + 12 = -11·x
x² + 11·x + 12 = 0
Solving the above equation using the quadratic formula, we get;
x = (-11 ± √(11² - 4×1×12))/(2 × 1)
x = (-11 ± √(73))/2
When x = (-11 + √(73))/2, y = 12/((-11 + √(73))/2) = 24/(-11 + √(73))
When x = (-11 - √(73))/2, y = 24/(-11 - √(73))
The two combination of numbers that multiply to be 12 and add to be -11 are;
(-11 + √(73))/2 and 24/(-11 + √(73)), and (-11 - √(73))/2 and 24/(-11 - √(73))
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Joy's math certificate is 10 inches tall and 13 inches wide. Joy wants to put the certificate in a fancy frame that costs $3.00 per inch. How much will it cost to frame Joy's math certificate?
In perimeter, The cost to frame Joy's math certificate in a fancy frame is $138.00.
The dimensions of Joy's math certificate are 10 inches tall and 13 inches wide.
Joy wants to frame it in a fancy frame that costs $3.00 per inch.
To determine the total cost of framing the certificate, we need to find its perimeter and then multiply that by the cost per inch.
The perimeter of the certificate is:
Perimeter = 2 × (height + width)
Substituting the given values, we get:
Perimeter = 2 × (10 + 13)Perimeter = 46 inches
Therefore, the total cost of framing Joy's math certificate is:
Total cost = Perimeter × Cost per inch
Total cost = 46 × 3.00Total cost = $138.00
Thus, the cost to frame Joy's math certificate in a fancy frame is $138.00.
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4 oranges at Juicy Deals grocery store cost $6. For the price of $15 you can buy 10 oranges. True or false: The relationship
between the number of oranges and their price is proportional.
Answer:
the answer is true.
4/6
10/15
Danny is building a pyramid modeled after one of the great pyramids of Giza in Egypt .The great pyramid has a height of 480 feet and a square base with each side measuring 755 feet if Danny builds the pyramid to one hundredths (1/100) the size what will the volume be for his pyramid
Answer:
91.204 cubic feet
Step-by-step explanation:
We are given that
Height of great pyramid, h=480feet
Side of square base, a=755 feet
Height of Danny's pyramid, h'=480/100 feet
Side of square base of Danny's pyramid, a'=755/100 feet
We have to find the volume of Danny's pyramid if the volume of Danny's pyramid is 1/100 the size of great pyramid.
We know that
Volume of square base pyramid, V=\(\frac{1}{3}a^2h\)
Where a= Side of base
h=Height of pyramid
Using the formula
Volume of Danny's pyramid=\(\frac{1}{3}\times(755/100)^2(480/100)ft^3\)
Volume of Danny's pyramid=91.204 cubic feet
I need help quick
Thx in advance
Answer:
5) 119 degrees
6) 25 degrees
7) 45 degrees
8) 115 degrees.
Solve the equation (show work if possible)
Answer:
-10 is right answer
Step-by-step explanation:
see in attached picture
hope it helped you:)
Answer:
\( \frac{r}{2} + 2 = - 3\)
\( = ) \frac{r + 4}{2} = - 3\)
\( = )r + 4 = - 6\)
\( = )r \: = - 6 - 4\)
\( = )r \: = - 10\)
A 20-foot-long footbridge has two diagonal supports that meet in the center of the bridge.
Each support makes a 65° angle with a short vertical support.
65
20 ft
65
What is the length x of a diagonal support, to the nearest tenth of a foot?
X≈
feet
The length x of a diagonal support, to the nearest tenth of a foot is; 11 ft
How to use trigonometric ratios?Let us say the side opposite to the 25° angle is a, in both triangles. The side opposite to the 65° angle is b, but we already know the length of b as it is 20/ 2 = 10 ft.
We should find the length of a using trigonometric ratios, and by Pythagorean Theorem, determine the length of x.
Thus;
a = tan 25 * ( 10 )
a ≈ 4.663 ft
b = 10 ft
By Pythagorean Theorem,
a² + b² = x²
4.663² + 10² = x²
21.74 + 100 = x²
x² = 121.74
x ≈ 11 ft ( to the nearest foot )
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Perform the indicated operations and simplify.
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
Let's simplify the expression step by step: Expand the squared term:
(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²
Expand the second term:
3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)
Expand the third term:
x(3x + 4y + 3) = 3x² + 4xy + 3x
Now, let's combine all the expanded terms:
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x
Combining like terms:
= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x
= 7x² - 5xy + 5y² + 3x
The simplified form of the expression is 7x² - 5xy + 5y² + 3x.
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Determine the value of x in the figure below.
Answer:
theres no picture u didnt put it
Answer: theres no picture
Step-by-step explanation:
Solve each Algebraic Equation
x-27=56
y+14=83
k+53=124
a-27=90
q+67=118
35+x=44
58+p=16
Answer:
x=83
y=69
k=71
a=117
q=51
x=9
p=-42
Step-by-step explanation:
use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and p0 are positive constants, approaches the equilibrium solution p(t) ≡ a b as t approaches [infinity].
The logistic model is a mathematical function that depicts how a limited quantity grows. To use a sketch of the phase line to argue that any solution to the logistic model approaches the equilibrium solution p(t) a b as t approaches infinity, the first step is to sketch the region where p(t) is increasing and decreasing.
The logistic model is a mathematical function that depicts how a limited quantity grows. This model is given by;\($$\frac{dp}{dt}=aP(1-\frac{P}{b})$$\) where a, b, and p0 are positive constants.To use a sketch of the phase line to argue that any solution to the logistic model approaches the equilibrium solution p(t) ≡ a b as t approaches infinity, let's follow the below steps.
Step 1: Sketch the phase lineThe logistic model's phase line can be illustrated by showing the regions where p(t) is increasing and decreasing. To depict the phase line, the equilibrium solution needs to be located at pb. For a solution to approach the equilibrium solution p(t) ≡ a b as t approaches [infinity], it implies that the solution must be to the right of pb on the phase line. As the curve approaches infinity, it gets closer to the equilibrium solution p(t) ≡ a b, as shown in the below sketch.
Step 2: Use the sketch to argue any solution approaches equilibriumThe phase line indicates that any solution on the left-hand side of pb on the phase line will approach zero as time increases. Thus, the equilibrium solution p(t) ≡ a b is the only stable solution when t approaches infinity. Therefore, any solution to the logistic model below, where a, b, and p0 are positive constants, approaches the equilibrium solution p(t) ≡ a b as t approaches [infinity].
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Please hurry ill give brainlist
simplify. y/x √1/2y
Answer:
\(\frac{y^{2}}{2x}\)
Step-by-step explanation:
a) simplify
\(\frac{y^{2} }{2x}\)
Answer:
ez y² /2x
Step-by-step explanation:
PLEASE HELP NEED THIS NOW DUE IN AN HOUR!!
Write and simplify an expression to represent the perimeter of the triangle shown. What is the perimeter of the triangle if y equals 3 feet?
(Please show work)
The perimeter of the triangle if y equals 3 feet is 31 feet.
Given:
sides of the triangle are y+5, 4y-3 and 3y+5 feet.
y = 3 feet
Let a = y + 5 = 3+5 = 8.
so a = 8 feet.
b = 4y - 3
= 4*3 - 3
= 12 - 3
b = 9 feet.
c = 3y+5
= 3*3+5
= 9+5
c = 14 feet.
Perimeter of the triangle = a+b+c
= 8 + 9 + 14
= 17 + 14
= 31 feet.
Therefore the perimeter of the triangle if y equals 3 feet is 31 feet.
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I NEED HELP ASAP!!
How many boxes would Alan have to sell to earn exactly $700?
Answer: Alan would have to sell exactly 180 boxes.
Step-by-step explanation:
What is the slope shown below?
Answer:
5/8
Step-by-step explanation:
Slope = rise/run
In this problem:
rise = 5
run = 8
Therefore, Slope = 5/8
2- Which equations have no solution? Select all
that apply.
x + 3 = 2x + 3
8 = 2(x+4) − 2x.
5x-2x = -7x+1
2x-3 = 5x - 3-3x
4xx+6= 2(x+1)+x
Answer: E has no solution
Step-by-step explanation: It is a contradiction
what is the slope of y=17x+43
Answer:
17
Step-by-step explanation:
It is simple
As the slope is represented by m,
And the equation of line is
y=mx+c
Therefore, here m=17, which is the slope of the given eq.
Mr. Brown's class has 20 students. 6 of the students have blonde hair. What
percent of the students have blonde hair?
Answer:
30%
Step-by-step explanation:
6/20 = .3
.3 x 100 = 30
The altitude a in feet of a plain tea minutes after lift off is given by a equals 3480+600 how many minutes after lift off is the plane at an altitude of 21,000 feet
The plane will reach an altitude of 21,000 feet approximately 29.2 minutes after lift off. Rounded to the nearest whole minute, the plane will be at an altitude of 21,000 feet 37 minutes after lift off.
To determine the number of minutes after lift off when the plane reaches an altitude of 21,000 feet, we need to solve the equation a = 21,000, where "a" represents the altitude in feet. By substituting the altitude value into the equation and solving for the variable, we can find the number of minutes.
The given equation represents the altitude "a" of the plane in feet, given by a = 3480 + 600t, where "t" represents the time in minutes after lift off. We need to find the number of minutes when the plane is at an altitude of 21,000 feet.
By substituting a = 21,000 into the equation, we have:
21,000 = 3480 + 600t
To isolate "t," we subtract 3480 from both sides:
21,000 - 3480 = 600t
Simplifying, we get:
17,520 = 600t
Dividing both sides by 600, we find:
t = 29.2
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a fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem
By using the concept of bell shaped curve of normal distribution, it can be concluded that
The histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is given by
f(x) = \(\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}\)
Where z = \(\frac{x - \mu}{\sigma}}\) where \(\mu\) is the mean and \(\sigma\) is the standard deviation
A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.
Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
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vince brought6 boxes of worms to use as bait while fishing with his friends if each person uses exactly 3 8ths of a box of worms how many people can share the worms?
There are 16 people who share the worm.
How to calculate the number of people?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this illustration, Vince brought 6 boxes of worms to use as bait while fishing with his friends if each person uses exactly 3 8ths of a box of worms
The number of people who shared the works will be:
= Number of worms / Amount collected by each person
= 6 ÷ 3/8
= 6 × 8/3
= 16
In conclusion, 16 people shared it.
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A high school drama club is performing a musical to benefit a local charity. Tickets are $5. They also receive donations if $500. They wants to raise at least $2000. How many tickets should they sell to reach their target
Answer: 300 tickets
Step-by-step explanation:
The drama club wants to raise at least $2,000. They have already received donations of $500 so the amount left till target is:
= 2,000 - 500
= $1,500
Tickets are being sold at $5 so the number of tickets needed to get to $1,500 is:
= 1,500/5
= 300 tickets
x y 3 9 6 18 9 27 12 36 The table shows a proportional relationship between x and y. What is the unit rate of y per x? A) 1 B) 3 C) 6 D) 9
Answer:yes
Step-by-step explanation:
It does show a proportion relationship because it has an upward growth of approximately 5.99999483838and 6x so if you do that together in your calc then you can get that answer please vote 5 stars.
For a scientific experiment, a physicist must make sure that the temperature of a metal does not get colder than −42°C or the metal will not be usable. The physicist changes the metal's temperature at a steady rate of −2°C per hour. Part 1 out of 3 Let t represent time in hours. Enter an inequality. Use the fact that the rate of change in temperature times the number of hours equals the final temperature.
The inequality can be written as -2t ≥ -42
To represent the temperature of the metal as a function of time and establish the given conditions, we can use the following inequality:
Rate of change in temperature * Number of hours ≥ Final temperature
In this case, the rate of change in temperature is -2°C per hour, and the final temperature should not be colder than -42°C. Let's represent the final temperature as T.
Therefore, the inequality can be written as:
-2t ≥ -42
Here, t represents time in hours, -2t represents the rate of change in temperature times the number of hours, and -42 represents the final temperature.
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the angle is 11/12 on a circle
Here we will show you how to calculate the angle in degrees made by the hour hand and minute hand on a 12-hour clock at 11:12.
Before we continue, note that a clock is shaped like a circle and is composed of 360 degrees.
There are 60 minutes in an hour, and 360 degrees divided by 60 minutes is 6. Therefore, the minute hand moves 6 degrees per minute.
As you can see, the hour hand and minute hand showing 11:12 on the clock make an angle. We used the hands to make the pie chart below so it is easier to visualize what we are calculating.
The hour hand and minute hand on a clock showing 11:12 actually make two angles: The hour hand to the minute hand is outlined in blue, and the minute hand to the hour hand is outlined in red.
360 - (336 - 72) = 96 degrees
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What is the value of x?
Answer:
46°
Step-by-step explanation:
from large triangle:
let the third unknown angle be 'a'
then,
a+x+7+85=180
a=88-x
now,from small triangle,
let the third unknown angle be 'b'
then,
b+x+2x=180
b=180-3x
b=a (vertically opposite angles)
then,
180-3x=88-x
2x=92
x=46