Please help. I've been trying to answer this question but I haven't been successful.
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Equations
It's required to find the value of x that satisfies the conditions of the figure.
We have an equilateral triangle. We know it's equilateral because all of its interior angles have the same measure (look at the tick mark on each angle).
Recall the sum of the interior angles of any triangle is 180°.
If all the interior angles have the same measure, then each angle measures 180/3 = 60°.
One of the angles is assigned an expression of x. We can equate it to 60:
5x - 18 = 60
Adding 18:
5x = 78
Dividing by 5:
x = 78/5
x = 15.6
Answer: I do believe the answer is 15.6. Hope this helps! ^w^
Related Questions
The expression (222)(x?) is equivalent to z What is the value of p?
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SOLUTION;
Step 1:
[tex]undefined[/tex]Terry invested $2,200 in the stock market for 2 years. If the investment earned 12%, how muchmoney did Terry earn in 2 years?
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We will have that $2200 represent the 100%, then how much money does 12% represent.
In order to solve for the ammount of money we multiply the invested ammount ($2200) times the percentage we want to know (12%) and divide it by 100%, that is:
[tex]m=\frac{2200\cdot12}{100}\Rightarrow m=264[/tex]Here we can see, he earned $264 in those 2 years.
i need help with this asap please check work when done
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Given the parent function
[tex]y=\cos x[/tex]From the graph,
The range of the function is best modelled by the interval
Comparing the function with general equation of the cosine function,
[tex]B=1[/tex]The formula for the period is,
[tex]T=\frac{2\pi}{B}[/tex]There
Haven’t done this type of math before could use some help:)
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Third row:
The balance stays the same as the previous row ($337.52).
We have 12 days between 9/7 and 9/18, so we can calculate the product/sum as:
[tex]S=12\cdot337.52=4050.24[/tex]NOTE: the product/sum will be used to calculate the average balance for the month.
Fifth row:
The balance stays the same as the previous row ($399.78).
We have 11 days between 9/20 and 9/30.
Then, the product/sum is:
[tex]S=399.78\cdot11=4397.58[/tex]Total:
The total product/sum is:
[tex]S_{\text{Total}}=1937.60+337.52+4050.24+399.78+4397.58=11122.72[/tex]Average daily balance:
We can take the total product/sum and divide by the total amount of days.
[tex]\text{average daily balance}=\frac{11122.72}{30}=370.76[/tex]Finance charge:
[tex]\text{ finance charge}=\frac{1.25}{100}\cdot370.76=4.63[/tex]New balance:
[tex]\begin{gathered} \text{New balance = previous balance - payment/credits + finance charge + new purchases} \\ \text{New balance = }387.52-50+4.63+62.26=404.41 \end{gathered}[/tex]The new balance is $404.41.
Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 21 = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.10SI10310101
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We are given the following equation of a line.
[tex]-2x=0[/tex]Let us first solve the above equation for x.
Divide both sides of the equation by -2
[tex]\begin{gathered} -2x=0 \\ \frac{-2x}{-2}=\frac{0}{-2} \\ x=0 \end{gathered}[/tex]So, the solution is x = 0
This means that the two ordered pairs must contain the x-coordinate 0 and the y-coordinate can be any value you like.
For example:
(0, -5) and (0, 5)
Here the x-coordinate is 0 and the y-coordinate is -5 and 5.
Let us plot these ordered pairs and the line on the given graph.
Circumference of a circleThe radius of a circle measures 16 m. What is the circumference of the circle?Use 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
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Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
Multiply. (−5 2/5)⋅3 7/10. −19 49/50. −15 7/25. −9 1/10. -1 7/10
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To perform this multiplication, first, we have to transform the mixed numbers into fractions as follows:
[tex]-5\frac{2}{5}=-\frac{5\cdot5+2}{5}=-\frac{27}{5}[/tex][tex]3\frac{7}{10}=\frac{3\cdot10+7}{10}=\frac{37}{10}[/tex]Substituting these values into the multiplication, we get:
[tex]\begin{gathered} (-5\frac{2}{5})\cdot3\frac{7}{10}= \\ =(-\frac{27}{5})\cdot\frac{37}{10}= \\ =-\frac{27\cdot37}{5\cdot10}= \\ =-\frac{999}{50} \end{gathered}[/tex]This result can be expressed as a mixed number as follows:
[tex]-\frac{999}{50}=-\frac{950+49}{50}=-(\frac{950}{50}+\frac{49}{50})=-(19+\frac{49}{50})=-19\frac{49}{50}[/tex]
Algebra Find the value(s) of the variables in each kite.
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56º,34º
1) A kite is a quadrilateral that according to the following theorem:
2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.
3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following
So we can pick one triangle and write out the following according to the Triangle sum theorem:
[tex]\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ \frac{13x}{13}=\frac{91}{13} \\ x=7 \end{gathered}[/tex]4) Finally, let's plug into each one the quantity of x and get the measure of those angles:
PLEASE HELP I WILL MARK BRAINLIEST!!Which of the following equations is a linear function?A) 2x + 3y = 6B) y = x^2 + 1C) y=x^3D) x^2 + y^2 = 9
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Given data:
The given sets of equations.
The polynomial in which degree of the variable is 1 is said to be linear expression.
The first option 2x+3y=6 is only linear function.
Thus, the option (A) is correct.
Which describes a number that cannot be irrational?A. a number that represents the ratio of the circumference to the diameter of a circle B. a number that can be written as the ratio of two integers C. a number that can be used to solve an algebraic equation D. a number that represents the length of the diagnostic of a square
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a number that can be written as the ratio of two integers (option B)
Explanation:Irrational number cannot be written in the fractional form
Rational numbers can be written in the form of fraction
Checking the options:
a) Circumference = πd
where d = diameter
π = Circumference/diameter
π is an irrational number
b) A number written as ratio of two intergers can be written in the form of fraction
Hence, it is rational
c) A number that we can use in solving an algebraic equation can be any real number.
From a real number, we have rational and irrational numbers. So, there is the likelihood we get an irrational number
d) side of a square = a
diagonal² = a² + a²
length of diagonal of a square = √(a² + a²) = √2a²
This can also yield either irrational or rational numbers.
A number that cannot be irrational means a number that is rational.
From the option, the only one without doubt that it is rational is a number that can be written as the ratio of two integers (option B)
A figure is made up of a triangle and a square. The square andthe triangle have the same base of 9 inches. The triangle has aheight of 7 inches, what is the total area of the figure?
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To solve the exercise, it is helpful first to draw the situation that the statement describes:
The total area of the figure will be
[tex]A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}}[/tex]Then, we can calculate the area of the square using the following formula:
[tex]\begin{gathered} A_{\text{square}}=s\cdot s \\ \text{ Where s is one side of the square} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} s=9in \\ A_{\text{square}}=s\cdot s \\ A_{\text{square}}=9in\cdot9in \\ \boldsymbol{A}_{\boldsymbol{square}}\boldsymbol{=81in}^{\boldsymbol{2}} \end{gathered}[/tex]Now, we can calculate the area of the triangle using the following formula:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} b=9in \\ h=7in \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \\ A_{\text{triangle}}=\frac{9in\cdot7in}{2} \\ A_{\text{triangle}}=\frac{63in^2}{2} \\ \boldsymbol{A}_{\boldsymbol{triangle}}\boldsymbol{=31.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Finally, we calculate the total area of the figure
[tex]\begin{gathered} A_{\text{total}}=A_{\text{square}}+A_{\text{triangle}} \\ A_{\text{total}}=81in^2+31.5in^2 \\ \boldsymbol{A}_{\boldsymbol{total}}\boldsymbol{=112.5in}^{\boldsymbol{2}} \end{gathered}[/tex]Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.
3) An experiment is designed to compare the average salaries in a particular Position in two competing companies. The null hypothesis is assumed to be that there is no difference in the average salaries of empoty employees in a particular position in the two companies. What is the alternative hypothesis?
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Given:
There are two competing companies.
Required:
We need to find the alternative hypothesis
Explanation:
If the null hypothesis assumes equal average salaries (i.e. no difference), then the alternative can take on three cases:
A)
One mean is greater than the other
B)
One mean smaller than the other
C)
The means are not equal
Now here A and B sound the same, so I shoukd be more precise,
A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
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Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
Hi, can you help me answer this question please, thank you!
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From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?
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65 adult's ticket and 85 children's ticket was sold
Explanation:Let the number of tickets for children = x
Let the number of adults ticket = y
Total tickets = 150
x + y = 150 ....equation 1
The cost of tickets per child = $4.75
The cost of tickets per adult = $7.50
Total revenue from tickets = $891.25
Total revenue from tickets = The cost of tickets per child × number of children ticket +
The cost of tickets per adult * number of adults ticket
891.75 = 4.75(x) + 7.5(y)
891.75 = 4.75x + 7.5y ...equation 2
x + y = 150 ....equation 1
891.75 = 4.75x + 7.5y ...equation 2
Using substitution method by making x the subject of formula in equation 1:
x = 150 - y
Substitute for x in equation 2:
891.25 = 4.75(150 - y) + 7.5y
891.25 = 712.5 - 4.75y + 7.5y
891.25 = 712.5 + 2.75y
891.25 - 712.5 = 2.75y
178.75 = 2.75y
y = 178.75/2.75
y = 65
Substitute for x in equation 1:
x + 65 = 150
x = 150 - 65
x = 85
Hence, 65 adult's ticket and 85 children's ticket was sold
hello im stuck on this hw problem and need help ty
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The amount of money that Abdul is going to donate to the City Youth Fund is denoted by x, and the amount of money that Abdul is going to donate to the Educational Growth Foundation is denoted by y.
Since Abdul will donate up to $500, the sum of those amounts must be less or equal to 500.
[tex]x+y\leq500[/tex]It is not possible to donate less than zero, therefore, we also have the following constrains
[tex]\begin{gathered} x\geq0 \\ y\geq0 \end{gathered}[/tex]Abdul wants the amount of money donated to the Educational Growth Foundation to be at least 4 times the amount of money donated to the City Youth Fund, therefore, we have our final constrain
[tex]4x\leq y[/tex]Combining those four regions, the solution is their interception, which is
6. ΔABC is mapped onto ΔA'B'C' by a dilation at D. Complete the statement: The dilation of 4/3 is _____. a. a reduction b. an enlargement
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Dilation involves adjusting the size of an object or a figure, without altering its shape.
The object can be increased or decreased depending on its scale factor.
A scale factor less than 1 results in a figure of reduced dimensions whereas, a scale factor greater than 1 results in a figure or an object of enlarged dimensions.
In the ΔABC, a dilation of 4/3, which is greater than 1, will thus result into an enlargement.
The correct option is B.
1. Caitlyn is going away to college and will need to rent a truck to helpmove. The cost of the truck is $35 plus $0.79 per mile. If her collegeis 85 miles away and she budgeted $100 for the rental, will she haveenough money?
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1. Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
we know that
The equation in slope intercept form of this situation is
y=mx+b
where
m=$0.79 per mile
b=$35
y -----> is the total cost
x -----> the number of miles
so
y=0.79x+35
so
For x=85 miles
substitute
y=0.79(85)=35
y=$102.15
we have that
102.15 > 100
therefore
she not have enough moneyA point is chosen at random in the square shown below. Find the probability that the point is in the shaded circular region. Each side of the square is 6in, and the radius of the circle is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.
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We will have the following:
First, we determine the area of the square and of the shaded region, that is:
[tex]\begin{gathered} A_s=6in^2\Rightarrow A_s=36in^2 \\ \\ A_c=\pi(3)^2\Rightarrow A_c=9\pi in^2 \end{gathered}[/tex]Now, we will have that the probability will be of:
[tex]P=\frac{9\pi}{36}\Rightarrow P=\frac{\pi}{4}\Rightarrow P\approx0.79[/tex]So, the probability is approximately 79%.
The answers available are SSS SAS CPCTC and definition of congruence
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Solution
The diagram below will be of help
From the above, we have two sides to be equal and an angle to be equal
Therefore, the answer Side, Angle, Side (SAS)
the equation 5x+7=4x+8+x-1 is true for all real numbers substitute a few real numbers for x to see that this is so and then try solving the equation
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The equation 5x+7 = 4x+8+x-1 is true for all real numbers.
Solution for the equation is 5x + 7 = 5x + 7.
Given,
The equation; 5x+7 = 4x+8+x-1
We have to find the solution for this equation.
Here,
5x + 7 = 4x + 8 + x - 1 = 5x + 7
The equation is true for all real numbers;
Lets check;
x = 65 x 6+7 = 4 x 6 + 8 + 6 - 1
30 + 7 = 24 + 13
37 = 37
x = 155 x 15 + 7 = 4 x 15 + 8 + 15 - 1
75 + 7 = 60 + 22
82 = 82
That is,
The equation 5x + 7 = 4x + 8 + x - 1 is true for all real numbers.
The solution for the equation is 5x + 7 = 5x + 7.
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The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.
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Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:
[tex]\begin{gathered} \frac{12}{10}=\frac{6}{x}\rightarrow(1) \\ \frac{12}{6}=\frac{6}{y}\rightarrow(2) \\ \frac{6}{12}=\frac{3}{z}\rightarrow(3) \end{gathered}[/tex]Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:
[tex]\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}[/tex]Therefore the perimeter is as follows:
[tex]\begin{gathered} P=x+y+x=5+3+6=14 \\ P_{(KMP)}=14 \end{gathered}[/tex]Which number line shows the correct solution to 4y - 82-20 ? H 4 -3 -2 -1 0 1 2 3 4 5 HHH O > & -3 -2 -1 0 1 2 3 4 5 HH H -4 -3 -2 -1 0 1 1 2 3 4 5 H → -3 -2 -1 0 1 2 3 4 5
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To find which of the lines represent the solution we first need to solve the inequality:
[tex]\begin{gathered} -4y-8\ge-20 \\ -8+20\ge4y \\ 12\ge4y \\ \frac{12}{4}\ge y \\ 3\ge y \end{gathered}[/tex]the last line is equivalent as:
[tex]y\leq3[/tex]Now that we have the solution we can look at the line that represents it. The solution tells us that y is less or equal to 3, this means that the solutions are to the left of the number 3. Now, since the inequality is not an exact one that means that the 3 is also a solution, which also means that the circle over the 3 has to be a solid one.
With this in mind we conclude that the line representing the solution is the third option.
Segment RS is translated by (x+1, y-2) and then reflected over the x-axis. The resulting segment R" S" has coordinates R" (7,3) and
S" (2,7). What are the coordinates of the segment RS?
can someone pls help meee
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The coordinates of segment RS are obtained as R(6, -1) and S(1, -5) for the given translation.
What is termed as the reflection over the axis?The line of reflection is the point at which the image satisfy the axis of reflection. There are two kinds of reflections: x-axis reflections and y-axis reflections. Vertical reflections are reflections that cross the x-axis. Horizontal reflections are reflections that cross the y-axis.For the given question;
Segment RS is translated by (x+1, y-2).
Then, the image formed is again reflected over the x-axis to form R" S" has coordinates R" (7,3) and S" (2,7).
To find the measure of R and S, first find the x -axis reflection of R" S".
R" (7,3) = R'(7, -3)and S" (2,7) = S'(2, -7)As, RS was translated by (x+1, y-2).
Then, subtract 1 and add 2 to its coordinates.
R'(7, -3) = R (7 - 1, -3 + 2) = R(6, -1)S'(2, -7) = S(2- 1, -7 + 2 ) = S(1, -5)Thus, the coordinates of segment RS are obtained as R(6, -1) and S(1, -5).
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Find the equation for thefollowing parabola.Vertex (0,0)Focus (2, 0)A. 2x^2 = yB. y^2 = 8x2C. X^2 = ByD. y^2 = 8x
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To answer this question we need the equation of a parabola that uses the distance from the focus to the vertex.
This formula is,
[tex]4p(y-k)=(x-h)^2[/tex]where,
p is the distance from the focus to the vertex, and the point (h,k) is the vertex.
[tex]\begin{gathered} \text{focus (2,0)} \\ \text{Threrefore} \\ p=2 \end{gathered}[/tex][tex]\begin{gathered} \text{vertex (0 , 0)} \\ \text{Therefore,} \\ h=0 \\ k=0 \end{gathered}[/tex]Let us now substitute the data into the equation of the parabola,
[tex]\begin{gathered} 4\times2(y-0)=(x-0)^2 \\ 4\times2(y)=x^2 \\ 8y=x^2 \end{gathered}[/tex]Hence, the equation for the parabola is, x² = 8y.
Option C is the correct answer.
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
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Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.Regular deposit:$1300Interest rate:4.2%FrequencyannuallyTime:17 yearsFuture value: $
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SOLUTION
We will use the formula
[tex]FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack[/tex]Where FV represents the future value annuity
P = Periodic payment = 1300
r = interest rate = 4.2% = 0.042
n = number of periods = 17 years.
So we have
[tex]\begin{gathered} FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack \\ FV=1300\lbrack\frac{(1+0.042)^{17}-1}{0.042}\rbrack \\ FV=1300\lbrack\frac{(1.042)^{17}-1}{0.042}\rbrack \\ FV=31,341.485 \end{gathered}[/tex]Hence, the answer becomes $31,341 to the nearest dollar
In 2001, Rodney Hampton earned $75,200 as a self-employed worker. He also earned $41,350 as an employee. How much FICA tax did he pay for both earnings? Note:Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$14,668.88$14,577.25$14,324.09$14,225.50None of these choices are correct.
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Step 1: Rodney Hampton earned $75,200 as a self-employed worker
% tax rate for self employed = 15.3%
[tex]\begin{gathered} =15.3\text{ \% of \$75200} \\ =\frac{15.3}{100}\text{ x \$75200} \\ =11505.6 \\ =\text{ \$11505.6} \end{gathered}[/tex]Step 2: Rodney Hampton earned $41,350 as a employee worker
%tax rate for employee = 7.65%
[tex]\begin{gathered} =\text{ 7.65\% of \$41350} \\ =\text{ }\frac{7.65}{100}\text{ x \$41350} \\ =\text{ 3163.3} \\ =\text{ \$3163.3} \end{gathered}[/tex]Step 3: FICA tax paid for both earnings = $11505.6 + $3163.3
= $14668.875
=$14668.88
Hence FICA tax paid for both earnings = $14668.88
Two numbers sum to 61. Twice the first subtracted from the second is 1. Find the numbers.
Answers
x + y = 61
y - 2x = 1
y = 2x + 1
x + (2x + 1) = 61
3x + 1 = 61
3x = 60
x = 20
y = 61 - 20 = 41
Sharon's house, the library, and Lisa's house are all on the same straight road. Sharon has to ride her bike 1 3/5 miles to get from her house to the library and another 2 3/4 miles to get from the library to Lisa's house. How far does Sharon live from Lisa? Explain how you got your answer.
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Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
In the question ,
it is given that
distance between Sharon and Library is [tex]1\frac{3}{5}[/tex] miles .
distance between Library to Lisa's house is [tex]2\frac{3}{4}[/tex] miles .
So according to the question
distance between Sharon's house and Lisa's house = (distance between Sharon and Library) + (distance between Library to Lisa's house) .
On substituting the values from above ,
we get ,
distance between Sharon's house and Lisa's house = [tex]1\frac{3}{5}[/tex] + [tex]2\frac{3}{4}[/tex]
= (5+3)/5 + (8+3)/4
= 8/5 + 11/4
taking LCM as 20 and solving further we get
= 32/20 + 55/20
= 87/20
= [tex]4\frac{7}{20}[/tex]
Therefore , Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
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