ALGEBRA Michella Hong noticed that her gross pay per period increased by $2,800 when her employer changed from a bi-weekly pay plan to a monthly pay plan. What is Michelle's annual salary
Answer:
Her annual salary is $62,400
Step-by-step explanation:
Michelle Hong noticed that her gross pay per period increased by 2,800 when her employer changed from a bi weekly pay plan to a monthly pay plan.
Bi weekly is a check every 2 weeks, so she would get 26 checks per year.
Monthly would be 12 checks per year.
When she gets paid monthly her pay increased by $2,800 each check.
Let x be one bi-weekly paycheck.
The equation we get is:
12(x+2800) = 26x
Multiply the bracket by 12:
12x +33600 = 26x
Subtract 12x from both sides
33600 = 14x
Divide both sides by 14:
x = 33600/14
x = 2400
Her pay increased by 2800 each period:
2400 + 2800 = 5200 per check.
5200 x 12 months = 62400
Her annual salary is $62,400
Find the perimeter of the triangle. Round your answer to the nearest
hundredth.
W
X
Y
units
Since, we have to find the sides of the given triangle we will make it a right angle triangle.
Construction: Extend XY to 1 unit and name it Z and join the point W with Z.
Now, the triangle YWZ is a right angle triangle where
YZ = 1 unit
WZ = 3 units
Then [tex]WY = \sqrt{(YZ)^{2}+ (WZ)^{2} }[/tex] [By Pythagoras Theorem]
= [tex]WY = \sqrt{(1)^{2}+ (3)^{2} }[/tex]
= [tex]WY = \sqrt{(10) }[/tex]
= [tex]WY = 3.16[/tex] units
Now, the triangle XWZ is also a right angle triangle where
XZ = 3 units
WZ = 3 units
Then [tex]WX = \sqrt{(XZ)^{2}+ (WZ)^{2} }[/tex] [By Pythagoras Theorem]
= [tex]WX = \sqrt{(3)^{2}+ (3)^{2} }[/tex]
= [tex]WX = \sqrt{18[/tex]
= [tex]WX =4.23[/tex] units
Now, In triangle XYW
XY = 2 units
WY = 3.16 units
WX = 4.23 units
∴ The perimeter of the triangle XYW will be
XY + WY + WX
= 2 + 3.16 + 4.23
= 9.39 units
To the nearest hundred, 9.39 rounds to 9
⇒ The perimeter of the triangle XYW is 9 units.
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evaluate 14c 3d\dfrac14c 3d41c 3dstart fraction, 1, divided by, 4, end fraction, c, plus, 3, d when c
According to the given statement :
(1/4)c + 3d= 45/2 when c = 6 & d = 7
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as the denominator of a complex fraction.
How is a fraction made?Fractions can be used to represent decimals. Place your decimal number above its place value to convert it to a fraction. For instance, since the number six occupies the tenths place in the fraction 0.6, we must multiply it by 10 to get the comparable fraction, 6/10.
According to the given data:Evaluate (1/4)c + 3d
when c = 6 & d = 7
x = (1/4)c + 3d
putting c = 6
& d = 7
=> x = (1/4) * 6 + 3*7
=> x = 3/2 + 21
=> x = (3 + 42)/2
=> x = 45/2
=> x = 22.5
=> (1/4)c + 3d= 22.5 when c = 6 & d = 7
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Use the GCF and the Distributive Property to rewrite the following expression: 24 + 27. Please I need help
Answer:
= 6(4 + 5)
Step-by-step explanation:
GCF = The greatest common factor, example: GCF of 12 and 16 = 12 is divisible by all of these numbers. The factors for 16 are 1, 2, 4, 8, 16. The two numbers (12 and 16) share common factors (1, 2, 4). The greatest of these is 4 and that is the greatest common factor.
Distributive property = allows us to multiply the number by a group of numbers, which are added together. The distributive property is given by: a(b+c) = ab + ac
The Greatest Common Factor of 24 and 30 is 6 because it is the largest number they have together (24 = 6*4 and 30 = 6*5)
24 divided by 6 = 4
30 divided by 6 = 5
This fits B the most: 6(4 + 5)
Step-by-step explanation:
question 4(multiple choice worth 5 points) (04.02 lc) two functions, a and b, are described as follows: function a y
The rate of change of function A is 3 times the rate of change of function B.
What is rate of change of a function?To determine the slope of a graphed function, we use the average rate of change formula: Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change.Now,
Given:
For Function A, y = 9x + 4For Function B, rate of change = 4 and y intercept = 4To find: The number of times the rate of change of function A is, as compared to the rate of change of function B.
Finding:
According to the information given,
Rate of change = 3, i.e., b = 3 for function By- intercept = 4, i.e., c = 4Thus, by the slope-intercept form, given by: y = bx + c, the rate of change for function B is given by:
y = 3x + 4
Now, on comparison with function A, we can see that the rate of change of the function A is exactly thrice of that of function B.
Hence, The rate of change of function A is 3 times the rate of change of function B.
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(COMPLETE QUESTION)
(04.02 LC) Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4. How much more is the rate of change of function A than the rate of change of function B? 2 3 6 9
3yards 5 feet 6 inches X 7=
Answer:
1,218 Inches
101.5 Feet
33.8333333 Yards
Step-by-step explanation:
A 2:15 scaled pattern for a mural is 10 feet long. How long will the mural be?
The length of the mural is 75 feet.
How to calculate the value?From the information, it was stated that a 2:15 scaled pattern for a mural is 10 feet long.
Therefore, the length of the mural will be:
= 10 ÷ 2/15
= 10 × 15/2
= 75
Therefore the length of the mural is 75 feet
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Dodi has 2 cups of liquid starch and will use the entire amount. She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need (hint 2 cups = 16 fluid ounces
The maximum containers Dodi will use will be 3
She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need
number of containers is 3
Dodi has 2 cups of liquid starch each containers hold a maximum of 6 fluid ounces 2 cups = 16 fluid ouncesif containers hold maximum fluid ounceslet number of containers is x6x=16x=16/6but x is a number so x=3So minimum number of containers is 3The time period "equal" in math refers to two meanings, numbers, or quantities which can be the same. The equivalence of two such portions shall be denoted by a bar over an equivalent symbol or equivalent sign. It also means a logical equivalence among values or a fixed of quantities.
what is a equivalent instance?
The definition of equal is something that is essentially the same or identical to some thing else. An instance of equivalent is (2+2) and the wide variety four. due to the fact that 2+2= 4, these matters are equal.
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The likelihood of something occurring is measured in terms of probability, which is based on ______.
The possibility that something will occur, prior measures, and conventional objective measurements all influence the likelihood that something will occur.
What is probability and what types are there in total?
The study of probability is a field of mathematics that determines the probability of an event occurring, which is represented by a number between 1 and 0. When an event has a probability of 1, it can be said to be a certainty. For instance, if the coin lands flat, the likelihood that it will come up "heads or tails" is 1. There are no other possible outcomes. A probability of .5 indicates that there is an equal chance that an event will occur or not.
Probability can be quantitatively represented in the simplest form as follows: the total number of possible outcomes multiplied by the ratio of the number of occurrences of a targeted event divided by the sum of the occurrences and failures of occurrences:
P(a) = P(a)/[P(a) + P(b)]
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Find three consecutive numbers whose sum is 84
Answer:
27 28 29
Step-by-step explanation:
Let the first be n , and if they are consecutive then the next two numbers are n+1 and n+2.
n+(n+1)+(n+2)=84.
3n+3=84.
⇒3n=81.
⇒n=27.
Hence numbers are n,n+1,n+2→27,28 and 29
Write 2,204,000,000 in scientific notation.
Explaining How to Use Linear Palls and
Imagine two lines intersect. How can the properties of
linear pairs and vertical angles help to determine the
angle measures created by the intersecting lines?
Explain.
Angles that are vertical are opposite ones that only have one common vertex.
Two sets of vertical angles result from the intersection of two lines.
When two lines intersect, we obtain two linear pairs, which are two angles that make a straight line.
Knowing one of the angles formed when two lines intersect enables us to determine that the vertical angle, which is the angle directly across from it, has the same measurement.
Additionally, we know that the angle next to it, which creates a linear pair, will be added to it (add to 180), allowing us to discover its measure by subtracting it from 180.
Since they are both vertical angles, the remaining missing angle will be the same as this supplementary angle.
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since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one.
since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one. The statement is false.
What is the US Census?US Census is a typical comprehensive count of a population specifically: an annual population count conducted by the government.
Now,
According to the laws of the US, it is true that the law permits people to indicate multiple racial identities to the US Census, in order to complete the data and determine the population of the States.
Hence, it is false that: since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one.
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then he spent $34 on lunches the next week.how much was in his account then?
In linear equations, -6 was in his account then .
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).Kiran had $24 in her account
24-16=8
28-8=20 he deposited $20
he spent $34 on lunches in the next week.
28-34= -6 his account balance was -6
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The complete question is -
At the Beginning of the month Kiran had $24 in his school cafeteria account. Then he spent $34 on lunches in the next week. How much was in his account then?
can please answer this question
Answer: about 7300 thousand per month
about 1700 per week
10 an hour? it doesn't sound right but it doesn't go into detail about how many hours he works so i don't know but i hope it helps.
Step-by-step explanation:
choose the correct answer to fill in the blank. an outlier is an observation which is less than iqr or greater than q3 ( )times iqr.
Outliers are any observations that fall more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3.
Outliers:
While observing the data in the observations some of data may fall outside the general scope of the other observations. Such observations are called outliers.
Given,
An outlier is an observation which is less than IQR or greater than Q3 times IQR.
Here we need to find in Q1 and Q3 place variations.
When we use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3. Any values which fall outside of the identified fence are considered outliers.
To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3.
Like,
IQR = (1.5 - Q1)
IQR = (1.5 + Q3)
This gives us the minimum and maximum fence posts that we compare each observation to.
Therefore, any observations that are more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers.
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If f (x) = (x^2 − 3)^4, then f '(1) =
Answer:
f'(1) = -64
Step-by-step explanation:
To find f'(1), we will be finding the f'(x) first which means the first derivative of f(x), we can find the derivative by using chain rule to this function.
The formula of chain rule is:
[tex]\displaystyle f(u) = u^n \to f'(u) = nu^{n-1}\cdot u'[/tex]
In simple explanation, we derive normally (power rule) then multiply by the derivative of inside (u).
Applying the formula, we will have:
[tex]\displaystyle{f'(x)=4(x^2-3)^{4-1}\cdot (x^2-3)'}\\\\\displaystyle{f'(x)=4(x^2-3)^{3}\cdot 2x}\\\\\displaystyle{f'(x)=8x(x^2-3)^{3}}[/tex]
Substitute x = 1 in the f'(x):
[tex]\displaystyle{f'(1)=8(1)(1^2-3)^3}\\\\\displaystyle{f'(1)=8(1-3)^3}\\\\\displaystyle{f'(1)=8(-2)^3}\\\\\displaystyle{f'(1)=8(-8)}\\\\\displaystyle{f'(1)=-64}[/tex]
Kiara has $520 in her bank account. each week she deposits $80 and withdraws $35. gael has $310 in his account. each week he deposits $95 and withdraws $20. write and solve an equation to determine the week w when gael and kiara have the same amounts of money in their accounts.
The answer is D and the written answer is 7
HELP ME OUT QUICK THANK YOU !What is -78.6 (-2.4)?
A. -188.64
B. -32.75
C. 32.75
D. 188.64
Answer:
d) 188.64
Step-by-step explanation:
Let's solve the problem,
→ -78.6(-2.4)
→ -78.6 × -2.4
→ 188.64
Thus, option (d) is correct.
Answer:
D. 188.64 is the correct answer!
Step-by-step explanation:
PLEASE HELP T-T i can't do this
Answer:
Part A:
(0.20)(10) = (0.05)(x) + (0.40)(10 - x)
Part B:
5.7 litres of 5% and 4.3 litres of 40%
Step-by-step explanation:
Let's assume she will stick with 10 litres in total for her mixture. (Maybe that's the size of her container.)
Let the volume of 5% by x litres.
Therefore the volume of 40% will equal 10 - x.
Reason: 10 litres total, if we use 2 litres of the one, we'll use 8 litres of the other. Get it?
Moving along...
So:
(0.20)(10) = (0.05)(x) + (0.40)(10 - x)
Now we solve the equation...
2 = 0.05x + 4 - 0.4x
2 - 4 = - 0.35x
-2 = -0.35x
let's multiply both sides by 100 to get rid of the decimal
-200 = -35x
x = 200/35
x = 5.7 litres (volume of 5% solution needed)
volume of 40% = 10 - 5.7 = 4.3 litres
What are the ordered pairs of the solutions for this system of equations? y=x^2-2x+3
y=-5x + 1
The ordered pairs of the solutions for this system of equations is (-2,11) and (-1,6)
Two integers written in a certain order make up an ordered pair. As a result, we may define an ordered pair as a pair of components that appear in brackets and in a specific order.
These equations are composed of a line and a parabola. The intersection points between them must be located:
[tex]y=x^2-2x+3[/tex]
y=-5x+1
Thus,
[tex]x^2-2x+3=-5x+1[/tex]
[tex]x^2-2x+5x+3-1=0[/tex]
[tex]x^2+3x+2=0[/tex]
[tex]x^2+x+2x+2=0[/tex]
[tex]x(x+1)+2(x+1)=0[/tex]
x+2=0, x=-2
x+1=0, x=-1
Since the quadratic expression may be factored out, the following x-values represent the system's solution:
x=-2 and x=-1
Now, we may obtain the corresponding y values using either of the system's original equations. We decide to use a linear equation as an illustration:
When x =-2,
y=11
x=-1,
y=6
Thus the two points solution us (-2,11) and (-1,6)
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A car speeds down the interstate at 85
miles per hour. What is this speed in feet per
second? (1 mile
= 5280 feet)
Answer:
124.67 feet per second
Step-by-step explanation:
First: multiply the feet per mile by the amount of miles that the car is going in order to get the feet per hour
5280 x 85 = 448,800
Second: divide the answer from the first step by 60 in order to get the number of feet per minute
448,800 ÷ 60 = 7480
Third: divide the answer from the second step by 60 in order to get the number of feet per second
7480 ÷ 60 = 124.67
Over the interval 4 ≤ x ≤ 8, does f(x) or g(x)=2x^2+x-1 have a greater average rate of change? Show your work below.
The X coordinates for this interval should be 4, 8 with the y coordinates being 0, 14
I just don't understand what the difference between f(x) and g(x) is supposed to be
Answer:
Function g(x) has the greater average rate of change over the given interval.
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\sf \dfrac{f(b)-f(a)}{b-a}[/tex]
Given:
f(4) = 0f(8) = 14Therefore, the average rate of change for the function f(x) over the given interval 4 ≤ x ≤ 8 is:
[tex]\sf \implies\dfrac{f(8)-f(4)}{8-4}=\dfrac{14-0}{8-4}=3.5[/tex]
Work out values of function g(x) for x = 4 and x = 8:
[tex]\implies \sf g(4)=2(4)^2+(4)-1=35[/tex]
[tex]\implies \sf g(8)=2(8)^2+(8)-1=135[/tex]
Therefore, the average rate of change for the function g(x) over the given interval 4 ≤ x ≤ 8 is:
[tex]\implies \sf \dfrac{g(8)-g(4)}{8-4}=\dfrac{135-35}{8-4}=\dfrac{100}{4}=25[/tex]
Therefore, function g(x) has the greater average rate of change over the interval 4 ≤ x ≤ 8, as 25 > 3.5.
Mentally estimate the product of 313 and 489
Answer:
remember: we are rounding!
313 × 489
Where 313 ≈ 300
Where 489 ≈ 500
Step-by-step explanation:
300 × 500 = 150,000 because 3 × 5 = 15
Hope this helps!
Interpret the quote in the context of what you learned. (Finance)
"Life was a lot simpler when what we honored was father and mother rather than all major credit cards."
Answer: i knew this before but i forgot
Step-by-step explanation:
.
Please help me on this
Answer:
second left
Step-by-step explanation:
Darlene received $18.70 for 22 pounds of aluminum cans. How much did she receive per pound?
Answer:
$0.85/lb
Step-by-step explanation:
unit rate = dollar amount / pounds
unit rate = ($18.70)/(22 lb)
unit rate = $0.85/lb
Answer:
.85 per pound
Step-by-step explanation:
Simplify.
√{24 x²y³)
Answer:
2xy√6y
Step-by-step explanation:
I would like to know what is 1/3 + 3/4 + 1/2
- - - - - - - - - - - - - - - - - - - - - - - -
Work below. :)
- - - - - - - - - - - - - - - - - - - - - - - -
First, find a common denominator. You can do so by listing the denominators' factors and finding a common number. (For the sake of space I'll skip).
1/2 = 6/12
3/4 = 9/12
1/3 = 4/12
Now, simply add the top numbers (aka numerator) but keep the denominator the same.
6 + 9 + 4 = 19
19/12 is an improper fraction, so make it proper.
1 7/12
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck!
~pinetreee
what is the value of the quantity 46-6squared ÷ 4
Answer:
400
Step-by-step explanation: