Using proportions, it is found that the deducted amounts each year are given as follows:
Social Security: $1,837.68.Medicare: $429.78.What is the missing information?The tax rates are missing, and they are given as follows:
Social Security: 6.20% = 0.0620.Medicare: 1.45% = 0.0145.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Considering that a year has 52 weeks, her yearly salary is given as follows:
52 x 570 = $29,640.
Considering the tax rate, the deducted amount for Social Security is given by:
0.0620 x 29640 = $1,837.68.
Considering the tax rate, the deducted amount for Medicare is given by:
0.0145 x 29640 = $429.78.
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Suppose ∠4 and ∠ 5 form a linear pair.
If m ∠1=2 x, m ∠2=3 x-20 , and m ∠3=x-4 what is m ∠3 ?
A. 26° B. 28° C. 30° D. 32°
Option C: The value of m ∠3 is 30° (C).
As per the question, ∠4 and ∠5 form a linear pair. Therefore the sum of ∠4 and ∠5 is 180° so, so the sum of the remaining m∠1,m∠2, and m∠3 angles is 180°.
So, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° (as the total angle is 360°).
Now, m∠4 + m∠5 = 180°(∠4 and ∠5 form a linear pair). (∴ m∠1 + m∠2 + m∠3 = 180°). Now we will put the given values and will try to find out the value of x.
2x + (3x-20) + (x-4) = 180
[m ∠1 = 2 x, m ∠2 = 3 x-20, and m ∠3 = x-4]
or,
6x-24=180
or,
6x = 180+24
or,
6x = 204
or, x = 204/6
or. x = 34
As per the question we have to find out the value of m ∠3.
m ∠3 = 34° - 4° = 30° (as x = 30°)
So, m ∠3 is 30°.
If ∠4 and ∠ 5 form a linear pair. And, m ∠1=2 x, m ∠2=3 x-20, and m ∠3=x-4, the value of ∠3 is 30°. Therefore, Option C is the correct answer.
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The length of an animal's stride is the distance between two consecutive tracks. The average stride length of a duck is about 5 inches. Write a glide reflection that can be used to predict the location of the next track for the following animal tracks.
duck
The glide reflection ( x + 2.5 , y ) is that is reflected in the line that separates the left prints from the right prints.
A glide translation is what?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.Now, let's assume that the initial position is (x , y) .
Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:
average = 5/2 = 2.5
Thus, the glide reflection is ( x + 2.5 , y )
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Ariane feeds her kitten kkk grams of food 222 times in the morning and 222 times in the evening. She feeds her dog ddd grams of food 111 time in the morning and 111 time in the evening.
Which expressions can we use to describe how many grams of food Ariane feeds her animals per day?
Step-by-step explanation:
in the morning, 222k + 111d
in the evening, 222k + 111d
grams, g = 444k + 222d
five sixths divided by 5
[tex]\cfrac{5}{6}\div 5\implies \cfrac{5}{6}\div \cfrac{5}{1}\implies \cfrac{5}{6}\cdot \cfrac{1}{5}\implies \cfrac{1}{6}\cdot \cfrac{5}{5}\implies \cfrac{1}{6}\cdot 1\implies \cfrac{1}{6}[/tex]
Name three planes that intersect at point P
Name the intersection of plane PQO and plane NMP
Name three lines that intersect at point S
I points PM & Q collinear are they coplanar
There are points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.
What are the collinear points and the coplanar?Collinear points are defined as points that are along a straight line represented by a collinear. Because a straight line may be drawn continuously between any two points, they are always collinear. There can be a collinear relationship from three or more points, although it is not necessary.
We have given a line and a planar surface with points O, M, N, Q, P, S, and T.
Here three planes that intersect at point P which are PMN plane, PQM plane and QST plane.
Here three planes that intersect at point S which are STN plane, MNS plane and QST plane.
Here points P, M & Q collinear are not collinear because they didn't lie in the same line but they are coplanar.
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PLEASE HELP I DONT UNDERSTAND
Answer:
x = 16
Step-by-step explanation:
16 and x have the same length.
solve the equation
3(n+11)-5n = -2(n-12)+9
Answer:
infinite number of solutions
Step-by-step explanation:
3(n + 11) - 5n = - 2(n - 12) + 9 ← distribute parenthesis on both sides
3n + 33 - 5n = - 2n + 24 + 9 , that is
- 2n + 33 = - 2n + 33
since the expressions on both sides are the same then any value of n will make the equation true.
thus the equation has an infinite number of solutions
Answer:
Any real value. Infinite no. of solutions.
Step-by-step explanation:
Let's open the bracket first. Multiply the term outside the bracket with each term inside the bracket.
[tex]\Rightarrow[/tex] 3(n+11)-5n = -2(n-12)+9
[tex]\Rightarrow[/tex] 3n + 33 - 5n = -2n + 24 + 9
Now simplify the n terms on both sides
[tex]\Rightarrow[/tex] -2n + 33 = -2n + 33
Here both LHS and RHS are same. And the terms gets canceled. Any real value of n satisfy the above equation.
Find a₁ for each arithmetic series. S₈ =440 and d=6
An arithmetic sequence (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the passage/progression is constant.
Therefore, the expression for the nth term is,
an = a₁ + (n − 1) d
and in general
an = am + (n - m) d.
where d is the difference.
For an arithmetic series with initial term a₁ and difference between terms of d
an = a₁ + (n − 1) d
We are given some of the values,
d = 6 and
S8 = 440
So, we will put the values in the formula and calculate the desired value,
a1 = 440 = a1 + ( 8 - 1 ) * 6 = a1 + 42
a1 = 440 - 42 = 398.
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Can you help me in identifying m?
The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;
a) m ≈ 28.4
b) m ≈ 12.09
c) m ≈ 9.38
Which theorem can be applied to find the value of m?a) The given triangle, is a right triangle.
The length of the legs of the triangle are; 33 and 56.
According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;
l = √(33² + 56²) = 65
From the formula for the area of a triangle, we have;
Area of a triangle, A, equals half the base length multiplied by the height.
A = 0.5 × Base length × Height
For the right triangle, we have;
A = 0.5 × Leg 1 × Leg 2
Which gives;
A = 0.5 × 33 × 56 = 924
However;
A = 0.5 × l × m
Where;
l = The hypotenuse = The base length = 65
m = The height of the triangle
Which gives;
A = 0.5 × 65 × m = 924
m = 924/(0.5 × 65) ≈ 28.4
m ≈ 28.4b) The side m is parallel the 14 units long side.
The proportion the side m divides a side of the triangle = 3 and 19
Given that the triangle formed by m is proportional to the larger triangle, we have;
m/14 = 19/(19+3)
m = 14 × 19/(19+3) ≈ 12.09c) From the proportionality of similar triangles, we have;
m/16 = 17/(14+15)
m = 16×17/(14+15) ≈ 9.38Learn more about the proportionality of similar triangles here:
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Simplify the expression:
–10v–6–1
Find the distance between each pair of parallel lines with the given equations.
y=x-11 y=x-7
The distance between each pair of parallel lines with the given equations y = x-11 and y = x-7 is 4 units.
We can find the points passing through the lines
Hence,
The points passing through the line y = x - 11 are:-
Let x = 11
y = 11 - 11 = 0
(11,0)
and;
Let x = 12
y = 12 -11 = 1
(12,1)
The points passing through the line y = x - 7 are:-
Let x = 7
y = 7 - 7 = 0
(7,0)
and;
Let x = 8
y = 8 -7 = 1
(8,1)
Hence, using distance formula, the distance between the parallel lines will be:-
[tex]\sqrt{(1-1)^2+(12-8)^2} =\sqrt{0+16}=\sqrt{16} =4 units[/tex]
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Use a coordinate grid to write a coordinate proof of the following statement.
If the vertices of a triangle are A(0,0), B(2 a, b) , and C(4 a, 0) , then the triangle is isosceles.
c. Use the Distance Formula to write an expression for B C .
Distance between the points A and B are equal to distance between points B and C.
So, The given triangle is isosceles.
And, . By using distance formula we have to write an expression for BC as,
⇒ [tex]D_{BC} = \sqrt{4a^2+b^2}[/tex]
Here,
The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)
We have to check the triangle is isosceles.
And, Write an expression for BC.
What is Isosceles triangle?
When two sides of a triangle are equal then the triangle is said to be isosceles triangle.
Now,
The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)
We have to check the triangle is isosceles.
For this we use distance formula and prove that the two sides of triangle are equal.
Distance between the points A (0, 0) and B (2a, b) is;
[tex]D_{AB} = \sqrt{(2a-0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]
And, Distance between the points B (2a, b) and C (4a, 0) is;
[tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]
Hence, Distance between the points A and B are equal to distance between points B and C.
So, The given triangle is isosceles.
c. By using distance formula we have to write an expression for BC as,
⇒ [tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]
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Which expressions are equivalent to-2y-8+4y?
Answer:
The expression that is equivalent to -2y-8+4y is 2y-8.
This graph shows the amount of medicine in a patient after receiving an injection.
How much medicine was in the patient after `4` hours?
729 mg
144 mg
2/3 mg
4 mg
Answer:
144 mg
Step-by-step explanation:
Um yea anyone want to answer this for me
Your aunt bought a new car. After three months of car payments she owed a total®
of $22,275 to the bank for the car loan. After 12 months, she owed $18,900 to
the bank for the car loan. What was her average payment rate on the principal of
the car loan during this time?
The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.
Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.
What is the average payment rate?Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.
Now, the difference of payment = 22,275 - 18,900
= $3,375
The difference of time = 12 - 3 = 9 months
So, the payment per month = 3,375 / 9
= $375 per month.
Now, 375 x 12 = $4,500
Principal amount = 4,500 + 18,900
= 23,400
Rate = 375 / 23400 × 100
= 0.016 × 100 = 1.60%
Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.
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A squirrel can run a short distance at a rate of 4 3/4 miles in 15 minutes. A fox can run a short distance at a rate of 21 miles in half an hour. Which is faster, and how much faster in miles per hour?
35 mph= .58 of a mile per minute
21 miles in 30 minutes= .7 of a mile per minute
if you multiply by 60 to see the distance in the same amount of time:
rabbit: 35 mph
fox: 42
So the fox would run a greater distance in the time given. Hope this helps!
show ur work BRAINILEST if ur right
Answer: number 1. 4 number2. 7
Step-by-step explanation:
I hope this helps!
Compute the BMI 75 kg 6'1"
Evaluate the formula V = Bh/3 for each pair of values.
B = 118 m^2 , h = 66 m
Answer:
i just need a points thnkyuuuu
Use synthetic division to divide the polynomials.
Answer:
11
8z² + 9z + 12 + -------
z - 1
Step-by-step explanation:
x - c = x - 1
change the sign of -1 to +1
8z³ + z² + 3z -1
1 | 8 1 3 -1
↓ 8 9 12
-------------------------
8 9 12 11
8z² + 9z + 12 remainder of 11
I hope this helps!
Find the 17 th term of each sequence. a₁₆=18, d=5
The 17 th term of the Arithmetic Progression (AP) is found to be a₁₇ = 26.
What is the AP sequence for arithmetic progression?In Arithmetic Progression (AP), the difference between the two numerical orders is a constant value. Arithmetic Sequence is another name for it.
We'd come across a few important words in AP, denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP may also be characterized in concepts of common distinctions, as shown below.
The following is the formula for determining an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the given data in the question;
16th term; a₁₆ = 18
Common difference; d = 5
Then, the 17th term would be calculated as;
Use the common difference formula;
d = a₁₇ - a₁₆
a₁₇ = a₁₆ + d
a₁₇ = 21 + 5
a₁₇ = 26
Therefore, the value of the 17th term of a AP is found as 26.
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A recipe calls for 1 5/8 cups of milk to make 8 pancakes. The number of cups of milk needed to make 26 pancakes is?
Answer:
13 cups of milk I think
Step-by-step explanation:
Can someone please help answer the questions I posted 11 hours ago, I'll give 5 stars!!
What is the sum of the 9th square number and the 1st square number?
Answer:
sum is 82
Step-by-step explanation:
[tex]\sf \textsf{The 9th square number is }9^2 = 81[/tex]
[tex]\sf \textsf{The 1st square number is }1^2 = 1.[/tex]
In order to find the sum of these two square numbers, simply add them together:
[tex]\sf Sum = 81 + 1 = 82[/tex]
The sum of the 9th square number and the 1st square number is 82.
Worth 60 POINTTSS!!! PLEASE HELPP MEEE i need explanation on how u got it tho
Answer:
1.-150 250-400 is -150
2. 6570 6288+282=6570
3.123 because 102+21 is 123
Step-by-step explanation:
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help pleasee
In a right triangle, the sides are 1 cm and √3 cm. Calculate the measures of acute angles
Answer:
This will be a 30°-60°-90° triangle because the hypotenuse is 2 cm, which is twice the length of the shorter leg.
URGENT
The point (5,r) and (8,-14 lie on a line with slope -4 find the missing coordinate r
Workers in an office of 90 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away Frequency Angle
Pizza 29
a
Curry 9
b
Fish & chips 24
c
Kebab 16
d
Other 12
e
How many degrees represent 1 person?
Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.
Take-away Frequency Angle
Pizza 29 a
Curry 9 b
Fish & chips 24 c
Kebab 16 d
Other 12 e
The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be
∠a = 4 x 29 = 116°
∠b = 4 x 9 = 36°
∠c = 4 x 24 = 96°
∠d = 4 x 16 = 64°
∠e = 4 x 12 = 48°
Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.
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which multiplication expression is equal to 2/3 ÷ 1/2?
Answer:
2/3*2/1
this is the answer
Answer:
2/3 × 2/1
Hope this helps :)
Explanation below.
Step-by-step explanation:
To find the multiplication expression, use the Keep, Change, Flip (KCF) method.
