The cumulative frequency is the running total of the frequency; each value in the cumulative frequency column is the sum of the previous and current frequency values.
From the data on the number of children, the following can be calculated:
Table of Frequency:
No. of Children | Frequency 0 | 1 2 | 2 3 | 2 4 | 2 5 | 1
Table of Relative Frequency:
Children | Frequency | Relative Frequency 0 | 1 | 1/9 2 | 2 | 2/9 3 | 2 | 2/9 4 | 2 | 2/9 5 | 1 | 1/9
Table of Cumulative Frequency:
Child Count | Frequency | Cumulative Frequency
0 | 1 | 1 \s2 | 2 | 3 \s3 | 2 | 5 \s4 | 2 | 7 \s5 | 1 | 8
Because the cumulative frequency is the frequency's running total, each value in the cumulative frequency column is the sum of the previous and current values in the frequency column.
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Solve for
x
2
(
x
+
4
)
=
−
6
Answer: -7
Step-by-step explanation: multiply first then you have 2x+8= -6.
subtract 8 from both sides. you now have 2x= -14. divide by 2. X = -7 ( look at attached image if confused)
Can anyone tell me how to do this
The required dimensions in the figure are
angle FXD = 44 degreesEG = 14angle FZG = 21How to find the required dimensionsDG = FG = EG incenters
solving for angle FXD using SOH CAH TOA
The side XG is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
sin 22 = FG / XG
XG = 14 / sin 22
XG = 37.37
sin x = DG / XG = 14 / 37.37 hence x = 22
therefore angle FXD is 44 degrees
EG = DG = 14
angle FZG
< DYE + < FXD + < FZE = 180 sum of angles of a triangle
94 + 44 + < FZE = 180
< FZE = 180 - 94 - 44
< FZE = 42
< FZE = 2 * < FZG
< FZG = 42 / 2
< FZG = 21
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Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3. 143. 143, point, 14 for \piπpi.
units^3
3
Answer:
4 is there answer I think
Step-by-step explanation:
Please help answer this page asap can be without step by step.
Which is a reasonable domain for the function f(x) = 10x + 8?
Choices:
0 < x < 6
0 < x < 24
0 < x < 64
0 < x < 248
The domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.
The domain of a function is the set of all possible input values for which the function is defined. For the function f(x) = 10x + 8, the domain will be all real numbers greater than or equal to 0. This can be seen by examining the equation: if x = 0, then f(x) = 8. Therefore, the domain of the function will be all x values such that x ≥ 0. To calculate the upper bound for the domain, we can solve for x by subtracting 8 from both sides of the equation, resulting in 10x = -8. Dividing both sides by 10 gives us x = -0.8. Therefore, the domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.
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(1.0x10^3) and 2.0x10^5
The value for (1.0x10³) / 2.0x[tex]10^5[/tex] is 0.005.
What are Exponent and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
(1.0x10^3) and 2.0x10^5
We don't have any sign so we proceed with operation division
(1.0x10³) ÷ 2.0x[tex]10^5[/tex]
= (1.0x10³) / 2.0x[tex]10^5[/tex]
Suing exponents
[tex]a^m/ a^n= a^{m-n[/tex]
= 1/2 x [tex]10^{3-5[/tex]
= 0.5 x [tex]10^{-2[/tex]
= 0.5 / 10²
= 0.5 /100
= 0.005
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y=1/4x+1
y=1/4x-1
How many solutions does this system
of equations have?
One solution, because the slopes
are different.
No solution, because the slopes
are the same and the y-intercepts
are different.
Infinitely many solutions, because
the slopes are the same and the
y-intercepts are the same.
Answer:
No solution, because the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
The two equations are:
y = 1/4x + 1 and y= 1/4x - 1
Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1
1/4x cancels out of the equation and we get the absurdity:
1 = -1
This indicates no solution to the system of equations
Answer:
No solution, because the slopes are the same and the y-intercepts are different.
We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)
which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?a. V = π∫dc[f(y)]^2dyb. V = π∫dc[f(y)]dyc. V = π∫dc[f(y)]dy^2d. V = π∫dc[f]2dy
The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π ∫dc [tex][f(y)]^{2}[/tex]dy.
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
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The volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π∫dc [f(y)]² dy
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
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ind all values of for which this approximation is within of the right answer. assume for simplicity that we limit ourselves
Using the Taylor Remainder Theorem, the values of x ≤ 1.2145 for which this approximation is within 0.004458 of the right answer.
The function is f(x) = cos(x) at a=0.
The Taylor Series is:
f(x) = f(a) + f'(a)/1! (x - a) + f''(a)/2! (x - a)^2 + f'''(a)/3! (x - a)^3 + .............
Now, d/dx (cosx) = -sinx at a = 0
d/dx (cosx) = 0
d^2/dx^2 (cosx) = -cosx at a = 0
d^2/dx^2 (cosx) = -1
d^3/dx^3 (cosx) = sinx at a = 0
d^3/dx^3(cosx) = 0
d^4/dx^4 (cosx) = cosx at a = 0
d^4/dx^4 (cosx) = 1
d^5/dx^5 (cosx) = -sinx at a = 0
d^5/dx^5 (cosx) = 0
d^6/dx^6 (cosx) = -cosx at a = 0
d^6/dx^6 (cosx) = -1
Now putting the value
f(x) = 1 + 0/1! (x - 0) + (-1)/2! (x - 0)^2 + 0/3! (x - 0)^3 + 1/4! (x - 0)^4 + 0/5! (x - 0)^5 + (-1)/6! (x - 0)^6 + .............
Simplifying
f(x) = 1 - 1/2! x^2 + 1/4! x^4 - 1/6! x^6 + .............
|1/6! x^6| ≤ 0.004458
Multiply by 6! on both side, we get
x^6 ≤ 0.004458 × 6!
After solving
x ≤ 1.2145
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The complete question is:
Find T5(2): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a=0. Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.004458 of the right answer. Assume for simplicity that we limit ourselves to |x| ≤ 1.
What are the six multiples of 8?
There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.
How do you solve multiples of 8?Knowing the multiplication table for 8 is necessary in order to determine the multiples of 8. Multiples of 8 are created by multiplying 8 by any natural number, resulting in 8n, where n is any natural number. As a result, the pattern is as follows: 8, 24, 40, 56, 72, 88, 104.The numbers that divide 8 perfectly without leaving a residue are considered to be its factors. The four components of 8 are 1, 2, 4, and 8.2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, and 97 are the prime numbers from 1 to 100.To learn more about multiples refer to:
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why is it impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal?
Each decimal number has a unique bit structure that starts at 1 bit, that's why it is impossible to convert a decimal number to binary digit-by-digit as is achievable with hexadecimal.
It impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal because each decimal number has a separate bit structure that starts at 1 bit and goes quickly, it is difficult to convert a decimal number to binary string of 4 bits digit by digit.
However, since each hexadecimal number has a width of 4 bits, this is achievable. It is relatively easy to go back and forth between binary and hexadecimal. The comparable 4-bit binary string is used to replace each hexadecimal digit in the original number.
Hexadecimal Number FD13.
1111 1101 00010011 each hexadecimal digit with its corresponding 4-bit binary value.
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Find the slope using points: (-10, 6) and (-5, 8)
Answer:
Step-by-step explanation:
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:
slope = (8 - 6) / (-5 - (-10)) = 2 / 5 = 0.4
So the slope of the line through the points (-10, 6) and (-5, 8) is 0.4
:(help please..i dont understand it.
Answer:
Below
Step-by-step explanation:
A = qty 2 at 12.50 each = 25.00
B = 33.90 / 2 = 16.95 unit price
C = 31.00 / 6.20 = quantity 5
VAT is value added tax ...take the total 108.28 and multiply by 15% = 16.24
The table below shows that the number of miles driven by Parker is directly
proportional to the number of gallons he used.
Gallons Used Miles Driven
34
41
45
1305.6
1574.4
1728
How many miles can he travel on 44.2 gallons of gas?
The number of miles he can travel on 44.2 gallons of gas would be = 1697.28 miles
How to calculate the number of mile?The table shows that there is direct proportional relationship between the number of miles traveled and the number of gallons used by Parker. That is increase in the number of mile = increase in the number of gallons.
If 34 gallons = 1305.6 miles
44.2 gallons = X miles
Make X miles the subject of formula;
X miles = 44.2 × 1305.6/34
= 57707.52/34
= 1697.28 miles
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Which graph is a function of x?
find the curvature. r(t) = 9t i 7t j (2 t2) k
The curvature of a curve r(t) = 9t i 7t j (2 t2) k is 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2).
What do you mean by curvature?Curvature is a measure of the amount by which a curve deviates from being straight. It describes the degree to which a curve bends or twists at any point along its length.
In mathematics, curvature is a property of curves and surfaces that is used to describe their shape and local behavior. For example, the curvature of a circle is constant and is equal to the reciprocal of its radius. The curvature of a straight line is zero.
Curvature is a scalar quantity and is usually measured in units of inverse length, such as 1/meter. There are several ways to mathematically define and calculate curvature, including the concept of the curvature of a curve at a point, which is the rate of change of the direction of the tangent to the curve at that point.
The curvature of a curve is given by:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³
where r'(t) is the first derivative of r(t), r''(t) is the second derivative of r(t), and || || is the magnitude or length of a vector.
Given the curve r(t) = 9t i + 7t j + (2 t²) k, we can find its first and second derivatives:
r'(t) = 9 i + 7 j + 4t k
r''(t) = 4 k
So, the curvature of the curve r(t) is:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³ = ||9 i + 7 j|| × ||4 k|| / ||9 i + 7 j + 4t k||³ = 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2)
Since this expression depends on t, the curvature is a function of t, not a constant.
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determine if linear
An equation is considered linear if it is in the form of y=mx+b where m is the slope of the equation and b is the y-intercept.
Properties of Linear EquationsThere are several properties possessed by linear equations, which are as follows:
Adding and subtracting the numbers of the two sides will not change the value equation. Multiplication and division of the two sides does not change the value of the equation The value of the equation does not change if both sides are added or subtracted by the same number If an equation is moved, addition changes to subtraction, multiplication changes to division, and vice versa.Learn more about linear equation at
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All of the following are benefit of joining a profeional aociation or organization EXCEPT…\
The one which not the benefit of being a member of a professional organization is providing certificate examinations at discounted rate. The correct option is D.
Which is a benefit of joining a Professional Organization?Professional associations provide the better networking opportunities with people who are specifically in our industry. Whether we are looking to pursue employment opportunities, link with other industry professionals, or even looking for a mentor in our profession, the networking opportunities are invaluable.
Another benefits of joining in a professional organization is that it helps build the career portfolio of a professional. Organizations which can provide opportunities for speaking engagements, career specialization, publication and even scholarship and training programs abroad.
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Although part of your question is missing, you might be referring to this full question: All of the following are benefits of being a member of a professional organization, except:
A. providing a wide range of continuing education units.
B. publishing newsletters and magazines dealing with current issues and trends in healthcare.
C. providing tuition reimbursement.
D. providing certificate examinations at discounted rate.
help pls.. i am not getting the correct solution
The common chord has a length equal to 6 centimeters.
How to determine the length of a chord common to two circles
In this problem we find the case of two circles of different radii (r₁ = 5 cm, r₂ = 3 cm), whose distance between centres is equal to 4 centimeters. We are required to determine the length of the chord common to the two circles.
First, determine one angle of a triangle by law of cosine:
cos θ = [(5 in)² - (3 in)² - (4 in)²] / [- 2 · (3 in) · (4 in)]
θ ≈ 90°
Second, determine the length of the common chord:
x = 2 · (3 cm)
x = 6 cm
The length of the common chord is equal to 6 centimeters.
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PLEASE HELP 30 pts for this
a) The length of the base is 10 units and the height is 7 units. The area is 35 square units.
B) The length of the base is 10 units and the height is 6 units. The area is 30 square units.
C) The length of the base is 10 units and the height is 3 units. The area is 15 square units.
D) The length of the base is 4 units and the height is 11 units. The area is 22 square units.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The base and height are highlighted in each triangle.
A)
The length of the base is 10 units.
The length of height is 7 units.
The area of the triangle is 1/2 × 10 × 7 = 35 square units.
B)
The length of the base is 10 units.
The length of height is 6 units.
The area of the triangle is 1/2 × 10 × 6 = 30 square units.
C)
The length of the base is 10 units.
The length of height is 3 units.
The area of the triangle is 1/2 × 10 × 3 = 15 square units.
D)
The length of the base is 11 units.
The length of height is 4 units.
The area of the triangle is 1/2 × 11 × 4 = 22 square units.
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trevor is making a poster for his science project he decides to use 1/2 of the poster for his pictures 3/8 for his hypothesis and 1/4 for the experiment process is this possible explain why or why not
No, it's not possible for Trevor to use 1/2 of the poster for his pictures, 3/8 for his hypothesis, and 1/4 for the experiment process.
How to show it is not possibleThis is discovered by addition of fraction
= 1/2 + 3/8 + 7/8
= 7/8
The fractions 1/2, 3/8, and 1/4 add up to 7/8, which is greater than 1.
Since the fractions represent parts of a whole poster, the total must be less than or equal to 1.
Therefore, Trevor needs to adjust the fractions so that their sum is less than or equal to 1.
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When marginal revenue is negative for a linear (inverse) demand function, increases in output will cause total revenues to:
a. increase
b. decrease
c. remain unchanged
d. there is not sufficient information to classify the elasticity of demand
Marginal Revenue is negative, the firm should consider reducing its output to increase its total revenue.
Therefore, correct answer will be a. increase.
Marginal Revenue (MR) is a crucial concept in economics that measures the change in a firm's total revenue as a result of selling one additional unit of output. MR is used by firms to make decisions about how much output to produce and what price to charge.
In a linear (inverse) demand function, MR is negative when the elasticity of demand is less than one, meaning that the demand for a product is relatively inelastic. In other words, as the firm increases output, the price will decrease, causing total revenue to decline.
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A shipping company makes cube-shaped boxes. Their basic box measures 1 foot per side. They want to know how to scale the basic box to build new boxes of various volumes. If the company wants a box with a volume of 8 cubic feet, by what scale factor do they need to dilate the box?
They need to dilate the box by a scale factor of ∛8.
What is scale factor?This refers to the number/amount by which a figure is bigger or smaller than the original figure.
Solving for scale factor they need to dilate the box:
The volume of a cube with sides of length "s" is given by the formula:
V = s³.
If the basic box has a volume of 1 cubic foot (V = 1), then a box with a volume of 8 cubic feet (V = 8) can be found by scaling the basic box by a factor of ∛8.
Hence, the scale factor is ∛8.
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solve the following system x1 −3x2 4x3 = −4 3x1 −7x2 7x3 = −8 −4x1 6x2 −x3 = 7
The solution of the system of equations is [tex]$x_1 = \frac{-400}{35}$, \\$x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]
The given system of equations can be written in matrix form as follows:
[tex]\begin{bmatrix}1 & -3 & 4 \\ 3 & -7 & 7 \\ -4 & 6 & -1\end{bmatrix}[/tex][tex]\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -8 \\ 7\end{bmatrix}[/tex]
We can solve for the unknowns [tex]$x_1$, $x_2$, and $x_3$[/tex] by using the Gaussian elimination method. The first step is to subtract 3 times the first equation from the second equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ -4 & 6 & -1\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-4 \\ -20 \\ 7\end{bmatrix}[/tex]
We can then subtract 4 times the first equation from the third equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 18 & -5\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -20 \\ -12\end{bmatrix}[/tex]
We can now add 10 times the second equation to the third equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 0 & -35\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -20 \\ 20\end{bmatrix}[/tex]
We can now solve for [tex]$x_3$[/tex] by dividing the third equation by -35, and the result is = [tex]\frac{20}{-35} = -\frac{20}{35}$.[/tex]
Therefore, the solution of the system of equations is
[tex]$x_1 = \frac{-400}{35}$, $x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]
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The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?.
The legs' lengths are 7 and 24 respectively. As a result, choice C is the right answer.
What is the Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most well-known triplets are (3,4,5).Completed question ;
The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?
A. 3 and 4
B. 5 and 5
C. 7 and 24
D. 10 and 15
Given data :
The hypotenuse of a right triangle measures 25.
A) 3²+4²= Square of the hypotenuse
25=Square of the hypotenuse
Hypotenuse=5 units
B) 5²+5²= Square of the hypotenuse
50=Square of the hypotenuse
Hypotenuse=5√2 units
C) 7²+24²= Square of the hypotenuse
625=Square of the hypotenuse
Hypotenuse=25 units
D) 10²+15²= Square of the hypotenuse
325=Square of the hypotenuse
Hypotenuse=√325 units
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The half-life of caffeine varies among individuals. For example, some medications extend the half-life to 8 hours. This means that 1/2 of the caffeine is eliminated from the bloodstream every 8 hours. Write a function for this new half-life time (assuming a peak level of 80 mg of caffeine) Determine the amount of caffeine in the bloodstream after: 1 hour? 5 hours? 10 hours? 20 hour?
The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.
What is caffeine?Caffeine is a natural chemical with stimulant effects.
Let's call the new half-life time for an individual with extended half-life as t. The function for the amount of caffeine (C) in the bloodstream after time t can be expressed as:
C(t) = 80 * (1/2)^(t/8)
Using this formula, we can determine the amount of caffeine in the bloodstream after different times:
1 hour:
C(1) = 80 * (1/2)^(1/8) = 80 * (1/2)^0.125 ≈ 79.28 mg
5 hours:
C(5) = 80 * (1/2)^(5/8) ≈ 64.51 mg
10 hours:
C(10) = 80 * (1/2)^(10/8) ≈ 51.37 mg
20 hours:
C(20) = 80 * (1/2)^(20/8) ≈ 25.68 mg
Therefore, The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
Step-by-step explanation:
Since the numerator is missing, you want to multiply the denominator onto the other side.
5 x 7 =35
x=35
Answer:
x=35
Step-by-step explanation:
Easy way to solve is making x/5 an improper fraction (fraction whose numerator is equal to or greater than its denominator.)
How I solved it was by multiplying 7×5=35, then I plugged the value into x making it (35/5)=7.
Now just make it a proper fraction, 35÷5=7, now we have 7=7.
Which expression can be used to represent the volume of this prism?
Responses
3 × 9 × 9 units³
2 × 3 × 9 units³
2 × 3 × 9 units³
3 × 3 × 18 units³
2 × 3 × 3 units³
A rectangular prism made up of unit cubes. There are 3 layers, and each layer is 9 units long and 2 units wide.
The volume of this prism = 2 × 3 × 9 units³.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given figure we get,
A rectangular prism made up of unit cubes.
There are 3 layers, and each layer is 9 units long and 2 units wide.
i.e. l = 9
w = 2
h = 3
so, the volume = V
we know, V= l.w.h
so, V = 9.2.3
Hence, The volume of this prism = 2 × 3 × 9 units³.
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Your realized income from your primary job is 2,034. 24/month. Your fixed expenses are 30% of your primary jobs realized income. You have a second job that pays $9. 50/hr with deductions of FICA (7. 65%), federal tax withhold (11. 5%), and a state tax withholding (7. 75%). If you want to save enough in the next 10 months to have an emergency fund that will cover 5 months using only 20% of your discretionary monies from your primary job, how many hours per month do you need to work at your second job to meet your monthly savings goal?
You need to work 84 hours per month at your second job to meet your monthly savings goal.
Fixed expenses = 2,034.24 x 30% = $610.72
Discretionary income = 2,034.24 - 610.72 = $1,423.52
Savings goal per month = $1,423.52 x 20% = $284.70
Net pay per hour = $9.50 - ($9.50 x 7.65%) - ($9.50 x 11.5%) - ($9.50 x 7.75%) = $7.33
Hours per month = $284.70 ÷ $7.33 = 84 hours.
To calculate, first find the number of your fixed expenses by multiplying your primary job income by 30%. This is $610.72. Then subtract your fixed expenses from your primary job income to find your discretionary income, which is $1,423.52. Multiply that by 20% to find the amount you want to save each month, which is $284.70.
Finally, divide that amount by your net pay per hour after taxes from your second job, which is $7.33, to find the number of hours you need to work, which is 84 hours.
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Help me please
Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
The value of x is 15
The value of y is 7.
The unknown sides:
x = 15
5y - 3 = 33
y + 9 = 16
x - 2 = 13
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Similar triangles mean the ratios of the corresponding sides are equal.
Now,
(5y - 3)/(y + 9) = 30/x = 26/(x - 2)
Taking two ratios.
(5y - 3)/(y + 9) = 30/x
5xy - 3x = 30y + 270
Taking two ratios.
30/x = 26/(x - 2)
30x - 60 = 26x
30x - 26x = 60
4x = 60
x = 15
Now,
Substituting x = 15
5xy - 3x = 30y + 270
5 x 15 x y - 3 x 15 = 30y + 270
75y - 45 = 30y + 270
75y - 30y = 270 + 45
45y = 315
y = 7
Now,
x = 15
5y - 3 = 35 - 3 = 33
y + 9 = 7 + 9 = 16
x - 2 = 15 - 2 = 13
Thus,
x is 15 and y is 7.
The unknown sides are 15, 33, 16, and 13.
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