Gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
As given in the question,
Gross salary of an individual is $150 000 a year
Percentage of tax on gross salary =30%
Amount of tax is equal to
= 30% of $150 000
= (30/100)× 150 000
= $45000
Net salary per year
= $(150 000 - 45000)
= $105000
Net salary per month
= $(105000/12)
= $8750
Therefore, gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
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A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
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Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.
For which value of x both functions give the same output?Here we have the functions:
f(x) = -2x +4
g(x) = 2x - 8
We want to find the value of x such that:
f(x) = g(x).
If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.
The graph can be seen in the image below.
There we can see that the graphs intercept at (3, -2), meaning that the solution of:
f(x) = g(x) is x = 3.
Which is the same thing that if we write:
f(x) = g(x)
-2x + 4 = 2x - 8
4x = 12
x = 12/4 = 3
x = 3
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slove using elimination10x + 8 y = 20 10 x + 2 y = -10
we have
10x + 8 y = 20 ------> equation A
10 x + 2 y = -10 ------> equation B
Multiply equation A by -1 both sides
so
-10x-8y=-20 -----> new equation A
Adds new equation A and equation B
\
--------------------
-8y+2y=-20-10
-6y=-30
y=5
Find the value of x
substitute the value of y in equation A or equation B or new equation A
10x + 8(5) = 20
10x+40=20
10x=20-40
10x=-20
x=-2
therefore
the solution is the ordered pair (-2,5)the graph of g(x) = (x + 2)2 is a translation of the graph of f(x) ___ by ___ units
The provided translated function, f(x), shifts left by two units on the horizontal axis.
Describe translation.One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.
The given graph equation for the translation, as per the query, is g(x) = (x + 2)²
The translation of the given quadratic function is: y = g(x) = (x + 2)²
Consequently, the parent function is written as y = g(x) = x2.
Additionally, the vertex should be known when graphing the translated function:
a(x - h)2 + k = y = g(x);
where the parent function is (0, 0) and the vertex values are (h, k).
(h, k) = is the vertex for the function that is provided (-2, 0)
This information causes the translation function to move the graph two units to the left.
Horizontal translation is the name given to the translation.
As a result, the given function, f(x), shifts horizontally, or left, by 2 units.
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a ferry charges $40 for each car and $8.50 for each person in the car. Does this situation represent a function?
Yes, This situation represent a function.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The cost of each car = $40
The cost of each person = $8.50
Let the number of car = x
The number of persons in a car = z
Then, Total cost of car = $40x
Total cost of persons in car = $8.50z
So, Total cost (y) = $40x + $8.50z
Thus, The function for this situation is;
y = $40x $8.50z
Clearly, This is a linear function with three variable.
Thus, This situation represent a function.
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The numerator of a rational number is 4 less than its denominator. If I is added to both its numerator and denominator, it becomes 2/3 Find the rational number.
The required rational number is 7/11.
let the denominator be x.
and since we are given that the numerator of a rational number is 4 less than its denominator, the numerator will be x-4.
working on the given condition, i.e. If I is added to both its numerator and denominator, it becomes 2/3
(x-4+1)/(x+1) = 2/3
further solving it by cross multiplication we get,
3(x-4+1)=2(x+1)
=> 3(x-3)=2x+2
=> 3x-9=2x+2
=> 3x-2x=9+2
=> x=11
=> x= 11 (denominator)
we know the numerator is 4 less than the denominator i.e.
11-4=7
thus the required fraction will be 7/11.
What are rational numbers?
A rational number is-" one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero".
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if f(x)=-5, what is x?
Answer:
x is any real number from -infinity to infinity.
are y=5x-4 and y=-5x+5 parallel or perpendicular
Answer:
Perpendicular
Step-by-step explanation:
It js seems right. i did one very similar and the awnser was Perpendicular
For
f(x) = 3x and g(x) = x4 + 2, find the following.
(b)(g ∘ f)(x)
Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)
The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)
Which of these equations is quadratic?An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.
The initial constant, “a,” cannot be 0, and this is an unbreakable rule.
How do you translate a graph into some equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
Thereafter draw a sloping triangle connecting the two spots you find on the line.
If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:
-2 = a(0+3)(0+1)
-2 = 4a
a = -1/2
So the equation can be written as y = -1/2 (x+3)(x+1)
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Check all the angles that are congruent to angle 5.
The angles congruent to ∠5 are as follows:
∠8∠1∠4∠9∠12How to find angles in parallel lines?According to the diagram, line l, m and n are parallel lines.
Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.
Hence, the angles that are congruent to ∠5 can be solved as follows:
∠5 ≅ ∠8 (vertically opposite angles)
Vertically opposite angles are congruent.
∠5 ≅ ∠1 (corresponding angles)
Corresponding angles are congruent.
∠5 ≅ ∠4 (alternate angles)
Alternate angles are congruent.
∠5 ≅ ∠9 (corresponding angles)
∠5 ≅ ∠12 (alternate exterior angles)
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3+2x1/10+4x1/1000 in standard form
Answer:
3.204
Step-by-step explanation:
3 + 0.2 + 0.004
Determine the distance between A(-3, 4) and B(2, -4).
5 units
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1=A(-3,4)
P2=B(2,-4)
Step 2
put the values into the equation
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}[/tex]Please help I’ll mark you as brainliest if correct!
The value of a in the magic square is 25
The value of b in the magic square is 3
The value of c in the magic square is 14
The value of d in the magic square is 7
What are the missing values?The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.
According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.
The three squares of the diagonal from left to right has all the complete numbers.
Sum of the the squares = 5 + 16 + 27 = 48
a = 48 - 18 - 5 = 25
b = 48 - 18 - 27 = 3
c = 48 - 29 - 5 = 14
d = 48 - 27 - 14 = 7
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Find the median 6, 13, 15, 9, 6, 11, 14
The median of a set of numbers is the number that appears in the middle after arranging the set of numbers in ascending or descending order
Step 1:Arrange the given values in ascending order.
Step 2. Find the number of observations in the given set of data. It is denoted by n.
Step 3. If n is odd, the median equals the [(n+1)/2]th observation.
The set of numbers given in the question are
[tex]6,13,15,9,6,11,14[/tex]By rearranging the numbers in ascending order, we will have
[tex]6,6,9,11,13,14,15[/tex]The numbers are 7 in number that is
[tex]N=7[/tex]Since the value of N is an odd number, then the median will be calculated using the formula below
[tex]\begin{gathered} \text{Median}=\frac{(n+1)}{2}th \\ \text{Median}=\frac{7+1}{2}th\text{ number} \\ \text{Median}=\frac{8}{2}th\text{ number} \\ \operatorname{median}=4th\text{ number} \end{gathered}[/tex]The 4th number after arranging the set of numbers is
[tex]=11[/tex]Hence,
The median of the set of numbers in the question = 11
The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data, using 7 classes.
Answer:
Step-by-step explanation:
The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data using 7 classes. Limits Boundaries 27-33 26.5-33.5 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 34-40 33.5-40.5 14 41-47 40.5-47.5 15 48-54 11 47.5-54.5 54.5-61.5 55-61 3 62-68 61.5-68.5 3 69-75 68.5-75.5 55
what is the slope of the line?
Answer:
slope :
[tex] \dfrac{y2 -y1}{x2 - x1} [/tex][tex] \dfrac{3 - 1}{0 - 1} [/tex][tex] \dfrac{2}{ - 1} [/tex][tex] - 2[/tex]Correct option - F
Donna bought a desk on sale for $343. This price was 35% of the original price.
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
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i need help with question 17
Answer:
[tex]42[/tex]Step-by-step explanation:
To find the median of a stem and leaf plot, use the equation:
[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]Therefore, for the given plot, there are 16 elements.
[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]When there are two middle values, the median is the mean of these two values:
[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]highest common factor of 106 and 104
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
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2(4x-3)-8-2x=4
someone please help me with this, fast
....................... .x=3
Help giving 100 points!!
Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope formula is the quotient of the difference in y-values and the difference in x-values.
Divide: (u² - 3u - 5) ÷ (u+3).
Answer:
u - 6 + 13/u+3
Step-by-step explanation:
Have a good day :)
One Serving of pancakes takes 2/3 cups of milk how many cups of milk with 24 servings for pancakes required
Answer:
Step-by-step explanation:
Given that:-
Since, Serving of 1 pancakes takes 2/3 cups of milk
Hence, serving of 24 pancakes takes (2/3)*24
=48/3
=16
So that; 16 cups of milk are required for serving of 24 pancakes.
Answer:
16 cups of milk
Step-by-step explanation:
Make a proportion
[tex]\frac{serrvings}{cups of milk}[/tex] = [tex]\frac{servings }{cups of milk}[/tex]
[tex]\frac{1}{\frac{2}{3} }[/tex] = [tex]\frac{24}{x}[/tex] cross multiply and solve
1x = [tex]\frac{2}{3}[/tex][tex](\frac{24}{1})[/tex] 1x is the same a x. 24 is the same as [tex]\frac{24}{1}[/tex]
x = [tex]\frac{48}{3}[/tex]
x = 16
4) A done relevant a bomb witha velocity of 20m/s horizotally from a hieght of 50m the ground clculate time
The time taken for the bomb to fall to the ground is 2.5 sec.
What is a projectile motion?In this case, the bomb is moving like a projectile and has projectile motion.A body can only move in a projectile motion when it is affected by gravity. A body moving as a projectile is a projectile motion.We model a particle as having zero acceleration (and thus constant velocity) when it is projected horizontally.The particle in this instance has a zero initial velocity and a constant downward vertical acceleration of g.Given:
Height (h) = 50 m
Horizontal velocity(u) = 20 m/s
Time (t) =?
We use, h = ut to determine the time
50 = 20 × t
Divide both sides by 20,
t = 50 / 20
t = 5/2 s ≅ 2.5 sec
Thus, the bomb will take 2.5 sec to land on the ground.
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The complete question is: "A bomb is projected horizontally downward from a height of 50m with a velocity of 20m/s. Calculate the time taken for the bomb to fall to the ground."
thank u plssssssss do it
Answer:
63
Step-by-step explanation:
23 + 94 = 117
180 degrees ( sum of all angles in a triangle)
180 - 117 = 63
Can someone please help with this
Answer:
x = 8
y = 8
Step-by-step explanation:
The two equations are:
x + y = 16 (1)
x = y (2)
Since x = y substitute for y in terms of x in (1):
x + x = 16
2x = 16
2x/2 = 16/2
x = 8
y = 8
Jackie deposited $500 in an account for 10 years at 6% interest.How much money did she earn?
After 10 years, the money dis she earn is $800 with the interest of 6%.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
Jackie deposited $500 in an account for 10 years at 6% interest.
Here we need to find the money did she earned.
We know that, the interest for the amount is 6%.
So, the amount after 10 years is,
=> 500 x (6/100) x 10
=> 30 x 10
=> 300
Therefore, the interest amount is 300.
So, the total amount she will receive after 10 years is,
=> 500 + 300
=> 800
Therefore, she will earn $800 after 10 years.
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At a speed of 7.2 km per 2 hours how far can you drive for 7 hours
A. 357
B.358.50
C.359
Answer:
Step-by-step explanation:
divide 7.2 by 2 so you have an hourly rate. Then you have 3.6, multiply that by 7 to get 25.2. Assuming its not in km cause that wouldn't make sense you would just have to convert it into whichever unit it would take