Jermaine's income tax was lowered by $640 as a result of the investment.
Investment calculationAssuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:
Tax savings = Contribution × Marginal tax rate
Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:
Tax savings = $3,200 × 0.20 = $640
Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.
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m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign
y=7x-3 what slope and y intercept
Answer:
Slope = 14.000/2.000 = 7.000 x-intercept = 3/7 = 0.42857 y-intercept = -3/1 = -3.00000
y intercept = -3
slope = 7/1
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 4.5 ft by 11.5 ft by 10.5 ft. The container is entirely full. If, on average, its contents weigh 0.4 pounds per cubic foot, and, on average, the contents are worth $4.60 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The value of the container's contents is approximately $983.25
What is the value of the container's contents?To find value of the contents, we must calculate its volume first.
Volume = length x width x height
Volume = 4.5 ft x 11.5 ft x 10.5 ft
Volume = 534.375 cubic feet
The container is full and its contents have a volume of 534.375 cubic feet. If its contents weigh 0.4 pounds per cubic, then, total weight of the contents is:
= Volume x Weight per cubic foot
= 534.375 cubic feet x 0.4 pounds per cubic foot
= 213.75 pounds
If the contents are worth $4.60 per pound on average, then the total value of the contents is:
= Weight x Value per pound
= 213.75 pounds x $4.60 per pound
= $983.25.
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State whether the decay is linear or exponential, and answer the associated question.
The value of a car is decreasing by 12% per year. If the car is worth $9,000 today, what will it be worth in two years?
_________________________________
= 12 × 9,000 ÷ 100= 1,080= 1,080 × 2= 2,160= 9,000 - 2,160= $6,840The Car Will Be Worth $6,840 After 2 Years_________________________________
Answer:
$6,840
Step-by-step explanation:
Find the equation of the quadratic function g whose graph is shown below.
The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the vertex and other points, we can determine the value of a as follows:
g(x) = a(x - h)² + k
-13 = a(-7 + 4)² - 4
-13 = a(-3)² - 4
-13 + 4 = 9a
-9 = 9a
a = -1.
Therefore, the required quadratic function is given by:
g(x) = a(x - h)² + k
g(x) = y = -(x + 4)² - 4
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(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24
The parent function is reflected across the x-axis and compressed by a factor 0.5
The rule used to obtain the transformed function is given as follows:
g(x) = -0.5f(x).
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The parent function in this problem is given as follows:
f(x).
The parent function is reflected across the x-axis, hence:
g(x) = -f(x).
The parent function is also compressed by a factor 0.5, hence:
g(x) = -0.5f(x).
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The company performed another experiment in which they tested three website designs to see which one would lead to the highest probability of a purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. what is the probability that a customer who visited made a purchase?
The probability that a customer who visited any of the three website designs made a purchase is 4.5%.
To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.
We can do this by taking the mean of the three probabilities:
Mean probability = (4.5% + 5.2% + 3.8%) / 3
= 13.5% / 3
= 4.5%
This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.
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Suppose in an orchard the number of apples in a tress is normally distributed with a mean of 300 and a standard deviation of 30 apples. Find the probability that a given tree has between 300 and 390 apples.
Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
How the probability is determined:Probability refers to the chance or likelihood that an expected event occurs out of many possible events.
Probability lies between 0 and 1, depending on the degree of certainty.
Mean = 300
Standard deviation = 30
Range = 300 to 390
Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
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NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83
Step-by-step explanation:
Here is a graph from Desmos....you should be able to see where the function is > 0
Mariana is making a large pot of pasta. She mixes together 518 pounds of pasta, 6 pounds of sauce, and 478
pounds of onions.
To find out how many 12
pound servings can she make, which two equations would you need?
A.
518+478+6=16
B.
518+478−6=4
C.
4÷12=8
D.
16÷12=32
E.
16×12=8
We need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
To find out how many 12-pound servings Mariana can makeWe need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
Equation C shows that each serving is 1/3 of a pound
Equation D shows that Mariana can make 4/3 servings
Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.
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7) If a professor can grade 5 essays in 40 minutes, the professor can grade 32 essays in 256 minutes. (10pts)
O True
O False
Answer:
O True
Step-by-step explanation:
Unit rate of essays/minute:
40 minutes / 5 essays = 8 essays/minute
256 essays / 32 minutes = 8 essays/minute
The unit rates are equal.
Answer: O True
Kadeesha borrowed some money from her friend in order to help buy a new video
game system. Kadeesha originally borrowed $120 and agreed to pay back her friend
$8 per week. Make a table of values and then write an equation for L, in terms of t,
representing the amount Kadeesha owes her friend after t weeks.
Number of Weeks Amount of Money Owed
0
1
2
3
You must answer all questions above in order to submit.
attempt 1 out of 2
An equation for L, in terms of t, representing the amount Kadeesha owes her friend after t weeks is L = 8t + 120.
The table of values is as follows;
Number of Weeks Amount of Money Owed
0 $120
1 $128
2 $136
3 $144
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the amount of money that Kadeesha borrowed originally and the number of weeks respectively, and then translate the word problem into a linear equation as follows:
Let the variable L represent amount of money that Kadeesha owed.Let the variable t represent number of weeks.Since Kadeesha originally borrowed $120 and agreed to pay back her friend $8 per week, a linear equation which can be used to model the total amount of money that Kadeesha owed is given by;
L = 8t + 120
When t = 0, the value of L is given by;
L = 8(0) + 120
L = $120.
When t = 1, the value of L is given by;
L = 8(1) + 120
L = $128.
When t = 2, the value of L is given by;
L = 8(2) + 120
L = $136.
When t = 3, the value of L is given by;
L = 8(3) + 120
L = $144.
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Need help. What is the x value pic attached below
The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2
Calculating the value of xFrom the question, we have the following equation that can be used in our computation:
f(x) = (1/3)^x - 2
When the value of f(x) is 7, we have
(1/3)^x - 2 = 7
So, we have
(1/3)^x = 9
Take the log of both sides
x = log(9)/log(1/3)
Evaluate
x = -2
Hence, the value of x is -2
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Can someone help me with this
Answer:
x = 23°
Step-by-step explanation:
We Know
The 67° angle + the x must be equal to 90°
Find the x.
Let's solve
67° + x = 90°
x = 23°
need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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(-6,-4), (0, -4), and (2,-4)
What is the equation of this line?
Answer: y = -4
Step-by-step explanation:
Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.
This means the equation of the line is:
y = -4
See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.
What are the values of x and y?
X=
Y=
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?
The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).
The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).
Substituting l = 1 m, we get
T = 2π√(1/9.81)
T ≈ 2.006 s.
In one day, there are
24 hours x 60 minutes/hour x 60 seconds/minute
= 86,400 seconds.
The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes
86,400/2
= 43,200 back-and-forth swings in one day.
The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is
2 x 12 degrees
= 24 degrees
= 0.419 radians.
Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is
1 meter x 0.419
= 0.419 meters.
Multiplying by the number of swings in one day, we get:
0.419 meters/swing x 43,200 swings/day
= 18,115.2 meters/day.
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There are 15 tables at a wedding reception,
5 of which have purple centerpieces.
1) What is the probability that a randomly
selected table will have a purple centerpiece?
◄) Write your answer as a fraction or whole
number.
Answer:
1/3
Step-by-step explanation:
There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.
5/15 is 5 out of 15. 5/15 simplifies to 1/3.
A surfer recorded the following values for how far the tide rose, in feet, up the beach over a 15-day period. 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24 Which of the following histograms best represents the data collected?
Find the areas of the trapezoids.
The areas of the trapezoids is,
A = 48 sq units.
Since, The formula to find the area of a trapezoid of a trapezoid is,
⇒ A = 1/2(b₁ + b₂ )h.
Hence, it is stated that the height of each unit is 2.
Now let's substitute the variables in the formula with the actual bases and heights as;
A = 1/2(8 + 4)8,
A = 6 × 8,
A = 48 sq units.
Thus, the areas of the trapezoids is,
A = 48 sq units.
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A soccer ball is kicked in the air off a 27.0-meter high hill. The equation h(t) = -2t^2 + 4t + 27 gives the approximate height h, in meters, of the ball t in seconds after it is kicked. Does the ball reach a height of 40 m?
The ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
To determine if the ball reaches a height of 40 meters, we can substitute h(t) = 40 into the equation and solve for t.
40 = -2t² + 4t + 27
Rearranging the terms, we get:
2t² - 4t - 13 = 0
We can solve for t using the quadratic formula:
t = [4 ± √(4² - 4(2)(-13))]/(2(2))
t = [4 ± √(176)]/4
t ≈ 3.38 or t ≈ -0.88
Since time cannot be negative, we can discard the negative solution. Therefore, the ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
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a grocery store sells a 7 oz bag of raisins for $1.10 and a 9oz bag of raisins for $1.46. Which size bag has the lower price per ounce?
To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.
For the 7 oz bag, the price per ounce is:
1.10 / 7 = 0.1571
For the 9 oz bag, the price per ounce is:
1.46 / 9 = 0.1622
Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.
Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is 4 : 20 which is 1: 5
Therefore, 4 of the next 20 horses that come to board should you expect to be white horses
2x+15-8=14
find the value of x
Answer:
x = 3.5
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]
Next, isolate the variable, x. First, subtract 7 from both sides of the equation:
[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]
Finally, divide 2 from both sides of the equation:
[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]
x = 3.5 is your answer.
~
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Answer:
[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]
Step-by-step explanation:
To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.
We can do this by first combining the constants on the right-hand side of the equation:
[tex]2x+15-8=14[/tex]
[tex]2x+7=14[/tex]
Next, we can isolate x by subtracting 7 from both sides of the equation:
[tex]2x=7[/tex]
Finally, we can solve for x by dividing both sides of the equation by 2:
[tex]x=\frac{7}{2}[/tex]
Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].
find the value of x in the cube
Answer:
3√3 ft or 5.20 ft
Step-by-step explanation:
The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.
x = L × √3
x = 3 × √3
x = 3 × 1.7
x = 5.20 ft
The electrical signal created by a piece of test equipment at a specific point in time is described by the function v inst(t)=12xsin(360x60x6.3+79). What is the maximum voltage produced by the system?
The maximum voltage produced by the system is 12 volts.
The function given is:
[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]
To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.
Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.
First, calculate the value of the argument:
360 * 60 * 6.3 + 79 = 136080 + 79 = 136159
Now, substitute this value back into the sine function:
sin(136159)
The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:
136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22
Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.
Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.
So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:
Maximum voltage = 12 * 1 = 12 volts.
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