The annual income tax paid by the person is: $4,500.
Annual income taxUsing this formula
Annual income tax=[Salary÷(1-percentage deduction)]- Salary
Let plug in the formula
Annual income tax=[40,500÷(1-10%)]-40,500
Annual income tax=45,000-40,500
Annual income tax=4500
Therefore the annual income tax paid by the person is: $4,500.
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Sqrt -1+2 using a+bi
[tex]\sqrt{-1} + 2 = i+2 = 2+i[/tex]
After 5 years, how much will marcia have saved in interest by consolidating the two balances? a. $1,526.40 b. $2,422.80 c. $105.00 d. $227.40
The closest among the choices is Choice C. $105. Differences in amount may vary in the rounding off of the decimal numbers.
The complete question is given below as:-
Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses.
Card A
Card B
Amount
$1,879.58
$861.00
APR
14%
10%
Monthly Payment
$43.73
$18.29
After 5 years, how much will Marcia have saved in interest by consolidating the two balances?
a.
$1,526.40
b.
$2,422.80
c.
$105.00
d.
$227.40
What is income?The amount received by an employee by giving the service or work to any frim will be termed as the income.
Given:
Card A - 1,879.58 ; APR 14%; monthly -43.73
Card B - 861.00 ; APR 10% ; monthly -18.29
5 years x 12 months/yr = 60 months.
Card A = 43.73 x 60 = 2,623.80
Card B = 18.29 x 60 = 1,097.40
Total : 2,623.80 + 1,097.40 = 3,721.20
Lowest APR is 10%. monthly rate: 0.83%
Total Card balance: 1,879.58 + 861 = 2,740.58
A = P * (r(1+r)^n) / [(1+r)^n -1]
A = 2,740.58 * [0.0083 (1.0083)^60] / [(1.0083)^60 - 1]
A = 2,740.58 * 0.014/0.64
A = 2,740.58 * 0.022
A = 60.29 monthly payment.
60.29 x 60 = 3,617.40
Separate cards: 3,721.20
Consolidated: 3,617.40
Difference: 103.80
Therefore closest among the choices is Choice C. $105. Differences in amount may vary in the rounding off of the decimal numbers.
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Which of the following is an equivalent expression to the expression
a4
A
a12
B
C
7
Q12
2
HELP.
Answer:
D is the correct option.
All the best!
Find the measure of one interior angle of a regular polygon with 13 sides
Answer:
152.3 approximately
Step-by-step explanation:
A polygon with 13 sides (and angles too) would be called tridecagon
Now, the sum of interior angles in a polygon is calculated by dividing the number of angles minus 2 by 180 [(n-2)*180]
(13-2)/180 = 1.980 and to find what is the measure of one angle, we divide the sum by the number of angles the polygon has
1.980/13 = 152.3 approximately
slope of (6,1) (-3,8)
Answer:
Slope= - 7/9
Step-by-step explanation:
m=rise/run
m=8-1= 7
-3-6=-9
m=7/-9
- 7/9
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of
[tex]\star\mathrm{(6,1)}\star[/tex]
[tex]\star\mathrm{(-3,8)}\star[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The slope formula is a lifesaver when it comes to finding the slope of two points! :)Here's the formula:
[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}\star[/tex]
Where:
[tex]\star[/tex] y2 and y1 are y-coordinates
[tex]\star[/tex] x2 and x1 are x-coordinates
So substitute the values accordingly:
[tex]\star\mathrm{\cfrac{8-1}{-3-6}}[/tex]
Simplify!
[tex]\star\mathrm{\cfrac{7}{-9}}[/tex]
Which is the same thing as...
[tex]\star\mathrm{-\cfrac{7}{9}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Please help studying for finals
Answer:
C angle H = 75.4
Step-by-step explanation:
In order to find the measure of angle H we must first find the value of x
Firstly it's good to know that the sum of the angles in a quadrilateral always add up to 360 degrees
Knowing this we can create an equation.
Since the angle measures must add up to 360 degrees we know that angle F + angle E + angle H + angle G = 360
Plugging in the given expressions for each angle we acquire
14x - 11 + 5x + 21 + 6x + 16 + 8x - 7
We can now solve for x
==> combine like terms
33x + 19 = 360
==> subtract 19 from both sides
33x = 341
==> divide both sides by 33
x = 10 1/3
Now that we have identified the value of x and we can plug in x = 10 1/3 into the given expression of angle H and evaluate to get the measure
Angle H = 8x - 7
==> plug in x = 10 1/3
Angle H = 8(10 1/3) - 7
==> multiply 8 and 10 1/3
Angle H = 82.7 - 7
==> subtract 7 from 82.7
Angle H = 75.6
C is the closest answer
Answer:
C. m∠H = 75.4°
Step-by-step explanation:
all sides of a quadrilateral add up to 360°
So, (5x + 21) + (14 - 11) + (6x + 16) + (8x - 7) = 360
Add like terms:
33x + 19 = 360
33x = 360 - 19
33x = 341
x = 341/33
x = 10.33...
Substitute:
∠H = 8x - 7
∠H = 8(10.3) - 7
∠H = 75.4°
Which equations graph as circles?
x² + x + y² = 4
2x + x + y² = 8
x² + y² = 5
x² + x + y = 6
x² + y² + y = 1
Answer:
A, C, and D
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Simplify!! Please!!!
Answer:
.................................................
Step-by-step explanation:
edge 2022
A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.
Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.
If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?
Trenton will need
square feet of plywood.
The amount of plywood that he needs to buy will be 21 square feet.
What is the surface area of the triangular prism?Let the prism with a length of L of the rectangular surface.
And the dimension of the triangle is A, B, and C. Then we have
SA = 2(area of triangle) + 3(area of rectangle surface)
A triangular prism.
The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.
The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.
Then the area of the triangle will be
⇒ 1/2 x 2 x 1.5
⇒ 1.5 square feet
The area of the rectangles will be
⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5
⇒ 18 square feet
Then the surface area of the triangular prism will be
Surface area = 2 x 1.5 + 18
Surface arae = 3 + 18
Surface area = 21 square feet
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The following group of values was entered into the TVM solver on a graphing calculator
N=108; I%= 6.6 PV =; PMT=-620 FV =0; P/Y = 12; C/Y=12; PMT:END which of theses expressions with return the same value for PV
Based on the entries into the TVM solver, the expression that will return the same value for PV is [tex]\frac{(620) (( 1 + 0.066)^{108} - 1) }{(0.066) (1 + (0.066))^{108}}[/tex].
Which formula will give the same Present Value?The formula for present value for this series of cashflows is:
= [tex]\frac{(Payment) (( 1 + Interest rate)^{Number of years} - 1) }{(Periodic interest) (1 + (Periodic interest))^{Number of years}}[/tex]
Based on the P/Y and the C/Y being 12, the number of periods given in the graphing calculator will be the same in the formula, which is 108 periods.
The interest rate of 6.6% will also be the same in the formula.
The best option is therefore option B which has all these figures and so will give the same present value.
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Answer: 0.0055 and 108
aka ($620) ((1+0.0055)^108 -1 / (0.0055) (1+0.0055)^108
Step-by-step explanation: Just did it, Good luck! :)
Factor x³ + x² + x + 1 by grouping. What is the resulting expression?
○ (x²)(x + 1)
O (x² + 1)(x)
O (x² + 1)(x + 1)
O (x³ + 1)(x + 1)
Work Shown:
x³ + x² + x + 1
(x³ + x²) + (x + 1)
x²(x+1) + 1(x + 1)
(x² + 1)(x + 1)
The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.
The factored form of x³ + x² + x + 1 is (x²+1)(x+1).
What is Factorization?A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.
We have,
x³ + x² + x + 1
Now, making groups as
(x³ + x²) + (x + 1)
= x² (x + 1) + (x+1)
= (x²+1)(x+1)
So, resulting expression is (x²+1)(x+1).
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Josh wants to pour 70.83 grams of salt into a container. So far, he has poured 39.1 grams. How much more salt should Josh pour?
Answer:
31.73 grams
Step-by-step explanation:
70.83 g - 39.1 g = 31.73 g
Please help urgent!!!
Which statement about the functions is true?
The minimum value of f(x) is less than the minimum value of g(x).
f(x) and g(x) intersect at exactly one point.
f(x) and g(x) have the same y-intercept.
The x-intercepts of f(x) are common to those of g(x) .
The x-intercepts of f(x) are common to those of g(x) .
What is x-intercept?
The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
Choice 2 is not true. Point B is not on the parabola.
Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.
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Find the measure of angle A.
66°
x +49
x+83
Step-by-step explanation:
Since , internal sum of angle of triangle is 180°
So,
66 + x +49 + x+83 = 180
or, 198 + 2x = 180
or, 2x = 180 -198
or, 2x = -18
hence, x = - 9
Now angle A = x + 49
= (-9) + 49
= 40
Hence measure of angle A is 40°.
Answer:
40
Step-by-step explanation:
From triangle law ,
66 + x +49 + x+83 = 180
or, 198 + 2x = 180
or, 2x = 180 -198
or, 2x = -18
hence, x = - 9
Now angle A = x + 49
= (-9) + 49
= 40
Hence, answer is 40.
so what? idc abt ur feelings just awnser me
The measure of center that will be used to emphasize the average height of the students is frequency of the numbers.
Average height of the students
The average height of the students is calculated as follows;
Average = total height/number of students
total height = 135 + 130 + 170 + 170 + 160 + 90 = 855
Average = (855)/(6)
Average = 142.5 cm
From the given heights of the students, 170 cm has the highest frequency and will influence the average height more.
Thus, the measure of center that will be used to emphasize the average height of the students is frequency of the numbers.
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[100 POINTS] Find the values of x, y, and z.
x 's measure is already given
x=20°
y=x+zy=160+20y=180°Answer:
∡x = 20°
∡y = 160°
∠z = 160°
Step-by-step explanation:
Angles on a straight line sum to 180°
⇒ ∠z + 20° = 180°
⇒ ∠z = 180° - 20°
⇒ ∠z = 160°
The central angle measure equals the corresponding arc measure.
⇒ ∡x = 20°
⇒ ∡y = ∠z = 160°
suppose a normal distribution has a mean of 38 and a standard deviation of 2 what is the probability that a data value is between 37 and 41? round your answer to the nearest tenth of a percent
Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 38, \sigma = 2[/tex]
As a proportion, the probability that a data value is between 37 and 41 is the p-value of Z when X = 41 subtracted by the p-value of Z when X = 37, hence:
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 38}{2}[/tex]
Z = 1.5
Z = 1.5 has a p-value of 0.933.
X = 37:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{37 - 38}{2}[/tex]
Z = -0.5
Z = -0.5 has a p-value of 0.309.
0.933 - 0.309 = 0.624,
0.624 = 62.4% probability that a data value is between 37 and 41.
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Please help!!! answer the following questions, thanks:)
(you don't need to draw the venn diagram, I just need the questions below answered)
Answer:
hope you can understand
What is the area of a circular fountain that has a 6 ft. diameter?
A. 18.84 ft2
B. 28.26 ft2
C. 9.42 ft2
D. 254.34 ft2
Answer: B. 28.26 ft2
Step-by-step explanation: I did this in school and got it right.
Answer:
B. 28.26 ft²
Explanation:
Area of Circle = π(radius)²Here given:
diameter: 6 ftradius = diameter/2 = 6/2 = 3 ftArea of the fountain:
3.14(3)² = 28.26 ft²sin 30° right triangle
Answer:
The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides.
...
Related Links
Sin 0 Degree Trigonometry Formulas
Inverse Cosine Law of Sines Formula
how do i do this could you show step by step please?
The value of x from the given right triangle in rational form is 14√
SOH CAH TOA identityThis is a way of determining the sides and angles of a right triangles
From the given triangle
Opposite = 7√4 = 14
Hypotenuse = x
acute angle = 45 degrees
Using the theorem
sin 45 = 14/x
x = 14/sin45
x = 14√2
Hence the value of x from the given right triangle in rational form is 14√2
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Write the equation for the graph of the line
shown.
My answer is y= 2x-1 but I’m not sure if it’s right
Answer: Hope this explains everything for you!
y= -2x+3
Step-by-step explanation:
y= 2x-1 is wrong
First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).
y= 2x+3 (So that means -1 is actually 3)
Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.
So the equation of the line is actually y= -2x+3
Montraie has a coin collection. He keeps 10 of the coins in his box, which is 20% of the collection. How many total coins are in his collection?
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
How to calculate the quantity of coins in a collection
In this question we know the quantity of coins in a box and such coins are part of the coin collection. By definition of percentage we have the total quantity of coins in the collection:
x = 10*(100/20)
x = 50
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
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Help ASAP!
Solve the following linear system by graphing. 7x – 2y = −4
Y=−5
a (-2,-5)
b (-6,0)
c (1,5)
d (7,-4)
Please help me this is very hard the first person to help me get's marked as brainly but i need the correct answer
A conveyor belt carries supplies from the first floor to the second floor, which is 39 feet higher.
The belt makes a 60° angle with the ground. How far do the supplies travel from one end of
the conveyor belt to the other to the nearest foot? If the belt moves at 70 ft./min., how long
does it take the supplies to move to the second floor to the nearest tenth of a minute?
O 68 ft.; 1.0 min.
O55 ft.; 0.8 min.
O 45 ft.; 0.6 min.
O23 ft.; 0.3 min.
The supplies travelled 45ft and it took 0.6min to get to the next floor.
What is trigonometry?Trigonometry is the branch of mathematics dealing with the relationship between the sides of a triangle and the angles.
Analysis:
The supplies distance travelled, distance of first floor from second floor and the ground form a right angled triangle.
so that sin 60 = 39/distance travelled by supplies
distance travelled by supplies = 39/sin 60 = 39/0.866 = 45 feet.
speed = distance / time
time = distance / speed = 45/70 = 0.6 min
In conclusion, the distance and time time taken for the supplies to get to the next floor is 45feet and 0.6 min respectively.
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Using the net below, find the surface area
of the triangular prism.
am
6 cm
7 cm
7 cm
4 cm
4 cm
Surface Area = [?] cm²
The surface area of the triangular prism is 153 cm².
What is a triangular prism?Imagine you have a triangle. Now, extend it upward to form a stack of triangles atop one another. The triangular prism is a new three-dimensional object.Typically, when we refer to a triangle prism, we mean one whose stack faces upward; in this case, we are referring to a right triangular prism.The area of the triangular prism is equal to the sum of the areas of the rectangle and the triangle, hence the prism's area will be,Area = A + B + C
=(9 × 15) + (0.5×6×3) + (0.5×6×3)
= 135 + 9 + 9
= 153 cm²
Hence, the surface area of the triangular prism is 153 cm².
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what is the minimum and maximum mass of 1.5 kg
The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.
Minimum and Maximum mass measurement
The minimum and maximum mass measurement is determined from the uncertainty in the measurement.
For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;
2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg
minimum mass = 1.5 kg - 0.033 kg = 1.467 kg
maximum mass = 1.5 kg + 0.033 kg = 1.533 kg
Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.
The complete question is below:
what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?
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Can someone help me withthe full page I will offer a lot of points
#1
Scale ratio
10ft/1in#2
Unknown is actual length
So the ratio is
x/0.75#3
The proportion is
x/0.75=10/1#4
Must be multiplied with 0.75
#5
x=0.75(10)x=7.5ftActual length is 7.5ft
Answer:
Question 1
Given scale: 1 in = 10 ft
[tex]\textsf{Therefore, the scale as a ratio}=\sf \dfrac{\boxed{10}\:ft}{\boxed{1}\:in}[/tex]
Question 2
The ratio of the garden's actual length to its length in the drawing:
[tex]\sf \dfrac{x\:ft}{0.75\:in}[/tex]
Question 3
Therefore, the proportion is:
[tex]\sf \dfrac{10\:ft}{1\:in}=\dfrac{x\:ft}{0.75\:in}[/tex]
Question 4
Multiply both sides of the proportion by 0.75 to find x
Question 5
[tex]\begin{aligned}\textsf{Proportion}: \quad \quad \;\sf \dfrac{10\:ft}{1\:in} & = \sf \dfrac{x\:ft}{0.75\:in}\\\\\textsf{Mulitply both sides by 0.75}: \quad \sf 0.75\cdot \dfrac{10}{1} & = \sf 0.75 \cdot \dfrac{x}{0.75}\\\\\textsf{Simplify}: \quad \quad \quad \sf 7.5 & = \sf x\end{aligned}[/tex]
Therefore, the actual length of the garden is 7.5 ft
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function . f(x) = ln x
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
How to Interpret Graphs?We are given the function;
f(x) = In (x)
Now, from the given tiles and when we punch the respective values for the given functions, we can say that;
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
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