Using system of linear equations, the law firm employed 7 associate and 9 partners
System of Linear EquationThe system of linear equations can be defined as a set of two or more linear equations that have the same variables. Linear equations can be said as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
In this question, we have to write out two equations and solve for the unknown variable.
let;
x = associatey = partnerx + y = 16 ...eq(i)
400x + 1000y = 11800 ...eq(ii)
From equation 1
x = 16 - y ...eq(iii)
Put eq(iii) into equation (ii)
400(16 - y) + 1000y = 11800
6400 - 400y + 1000y = 11800
6400 + 600y = 11800
600y = 11800 - 6400
600y = 5400
y = 5400 / 600
y = 9
Put y = 9 in equation (i)
x + 9 = 16
x = 16 - 9
x = 7
The firm has 7 associate and 9 partners
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Could Someone Help Me with this rewrite dis equation into y=mx+b
y< -3/4x+2
The equation in the form of y=mx+b will be y= -3/4x+2
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that the inequality is y< -3/4x+2,
We have to write the inequality in the form of y=mx+b
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the equation in the form of y=mx+b will be y= -3/4x+2
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A specialty shop procures several grandfather clocks for $200 apiece and offers them to customers
or $568 each. What percentage is the mark-up?
Use the picture equation
How long is the hypotenuse of a right triangle 24 square inches in area and with one leg 6 inches long? A. 24 inches B. 18 inches C. 12 inches D. 10 inches
Answer:
D
Step-by-step explanation:
area of triangle = 1/2*B*H
Assuming its one leg we write
24 = 1/2*6*h
h= 8
With this info we can use Pythagoras Theorum
[tex]a^{2} = b^{2} + c^{2}[/tex]
[tex]x^{2} = 8^{2} + 6^{2}[/tex]
[tex]x^{2} = 100[/tex]
[tex]\sqrt{100}[/tex]
[tex]x = 10[/tex]
What is the domain of this function?
what is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2. statement (1) alone..
For the given statement about hundredth digit of the given decimal z the following statement is true:
Option E. statement (1) and (2) together are not sufficient.
As given in the question,
Let us consider decimal z is represented by k.lmn
Here hundredth digit of z is equal to m
Now,
(1) The tenths digit of 100z is 2.
100z
= 100(k.lmn)
=klm.n
This implies n = 2
(2) The units digit of 1,000z is 2.
1,000z
= 1,000(k.lmn)
= klmn
This implies n =2
From both the statements we are getting the value of n which is not sufficient to get the value of required 'm'.
Therefore, Option E is the correct answer which shows both the statements are not sufficient to get the value required hundredth digit of decimal z.
The complete question is:
What is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
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Which division equation represents the situation?
Answer: 6 divided by 2/3
Step-by-step explanation:
The division equation which represents the situation is 6 ÷ 2/3 = 9.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Division equation is the equation involving the operation of division.
The model shows there are 9 pieces that are each 2/3 feet long.
We can calculate the total length of the pieces using the multiplication equation.
9 × 2/3 = 6
Total length = 6 feet
Length of each piece = 2/3 feet
Number of pieces can be found using the division equation,
6 ÷ 2/3 = 9
Hence the division equation for the given situation is 6 ÷ 2/3 = 9.
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Add 3[tex]\frac{5}{6}[/tex]+(-1[tex]\frac{1}{6}[/tex] Write your answer as a mixed number in simplest form.
Answer: 2 2/3 or 8/3
Step-by-step explanation:
3 5/6 = 23/6
-1 1/6 = -7/6
23/6-7/6
16/6
simplify
8/3
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
3 [tex]\frac{5}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex] = [tex]\frac{23}{6}[/tex] ( [tex]\frac{6}{6}[/tex] is the same one)
1 [tex]\frac{1}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex]
Adding a negative number is like subtracting a positive number.
[tex]\frac{23}{6}[/tex] - [tex]\frac{7 }{6}[/tex] = [tex]\frac{16}{6}[/tex] 6 goes into 16 2 times with 4 left over
2 [tex]\frac{4}{6}[/tex] Divide the top and bottom by 2 to get
2 [tex]\frac{2}{3}[/tex]
A room is 9 feet by 12 feet. How far is it across from opposite corners?
A. 17
B. 14
C. 15
D. 11
13 Which situation could be modeled by a linear function?
(1) The value of a car depreciates by 7% annually.
(2) A gym charges a $50 initial fee and then $30 monthly.
(3) The number of bacteria in a lab doubles weekly.
(4) The amount of money in a bank account increases by 0.1%
monthly.
The situation could be modeled by a linear function is
(2) A gym charges a $50 initial fee and then $30 monthly.
What is a linear function?A linear function in mathematics is one that has either one or two variables and no exponents.
2) Let y be the total amount charged by the gym to a person for x months.
as the initial amount for every person is $30.
The gym charges [tex]50+30x[/tex] $ after x months.
Hence this is a linear equation.
The remaining situations cannot be expressed as a linear equation because they include percentages in them.
Every situation that has a percentage is an exponential function.
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Use the information in the table f (x), the graph g (x)and equation h (x) to evaluate the following expressions.
Drag and drop the most appropriate answer in the box provided.
Question 1
[tex](f \circ g)(-2)=f(-2) \cdot g(-2)=10 \cdot 3=\boxed{30}[/tex]
Question 2
[tex](g \circ h)(1)=g(1) \cdot h(1)=2(1^2 -9)=\boxed{-16}[/tex]
Question 3
[tex](g/f)(0)=\frac{g(0)}{f(0)}=\frac{0^2 -9}{6}=\boxed{-3/2}[/tex]
Question 4
[tex](h/f)(-3)=\frac{h(-3)}{f(-3)}=\frac{3^2 -9}{12}=\boxed{0}[/tex]
A line with a slope of 0 passes through the point (9, 8). What is its equation in slope-intercept form?
Answer: y = 0x + 8
Step-by-step explanation:
The slope-intercept form is y=mx + b
The slope is 0, and y-intercept is at (0,8)
So our equation is
y = 0x + 8
Please Help Me ASAP!!!!!!!!!
Answer: 6,3
Step-by-step explanation:
Answer:
6,3
Step-by-step explanation:
Are the lines A and B parallel? (The figure may not be drawn to scale). Please help!! Giving brainliest for whoever has the right answer
Answer:
Yes, they are parallel.
Step-by-step explanation:
61 + 119 = 180
One line is 180 degrees.
A fair spinner has 12 equal sections: 3 red, 5 blue and 4 green.
It is spun twice.
What is the probability of getting not green then green?
Answer:
2/9 = approximately 0.22.
Step-by-step explanation:
There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.
To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.
Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.
Write the linear equation of the following graph in slope-intercept form.
y =-1/2x
y=1/2x
y=-2x
y=2x
please help!!!!
The linear equation of the following graph in slope-intercept form will be; y=1/2x
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The slope of the line is calculated as follows:
m = Δy/Δx
To find the linear equation of the following graph in slope-intercept form.
Therefore, the slope of the line is;
m = Δy/Δx
m = 1/2
When we simplify it, then we get the equation as;
y=1/2x
Hence, The linear equation of the following graph in slope-intercept form will be; y=1/2x
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Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
Answer:
B) 10
Step-by-step explanation:
The triangles are congruent by HL. Thus, by CPCTC, [tex]x=10[/tex].
Gabe is the human resources manager for the Advanced Scientific Research Lab. He has to record the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab. Height distribution (cm) 178 163 174 186 154 167 167 181 159 165 177 191 158 Weight distribution (lbs) 157 163 190 187 183 173 184 189 193 192 177 173 168 13 Select the correct answer. What is the shape of the height and weight distribution? A. The height and weight distribution exhibit a negative and a positive skew, respectively. B. Both the height and weight distribution exhibit a positive skew. C. Both the height and weight distribution exhibit a negative skew. D. Both the height and weight distribution are symmetric about the mean. E. The height and weight distribution exhibit a positive and a negative skew, respectively.
Last option: The height and weight distributions, respectively, show positive and negative skews.
What is bar graph?Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.
There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.
[tex]\frac{change}{strating point } X 100%[/tex]
2.5 millions of books were sold in 1991.
Millions of books sold in 1992 equaled 3.4.
Change = 0.9 (in millions).
[tex]\frac{0.9}{2.5} X 100 = 36[/tex]%
The height and weight distributions, respectively, show positive and negative skews.
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helppp i need helpppp
he graph shows the number of pages in each chapter of a book that Josh is reading. A number line going from 2 to 28. 1 dot is above 2. 0 dots are above 4. 0 dots are above 6. 0 dots are above 8. 2 dots are above 10. 0 dots are above 12. 3 dots are above 14. 2 dots are above 16. 1 dot is above 18. 2 dots are above 20. 2. dots are above 22. 0 dots are above 24. 1 dot is above 16. 0 dots are above 28. Which statement is true about the effect of the 2-page introduction chapter? The outlier of 2 increases the median page count. The outlier of 2 increases the mean page count. The outlier of 2 decreases the median page count. The outlier of 2 decreases the mean page count.
The outlier of 2 decreases the mean page count.
What is mean and median?
The mean is that the variety you get by dividing the total of a collection of values by the quantity of values within the set.
In distinction, the median is that the middle variety in an exceedingly set of values once those values square measure organized from smallest to largest.
Main Body:
From the picture we can know that outlier of 2 does not effect the median page count.
But outlier of 2 decreases the mean page count.
it can be found out by taking mean
(1+2+3+2+1+2+2+1)/8= 1.75
and if we remove outlier of 2 ,then
(1+3+2+1+2+2+1)/7 = 1.86
Hence ,the outlier of 2 decreases the mean page count.
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Answer:
the answer is d
Step-by-step explanation:
3. Apply Math Models Cynthia earns $680 in
commissions and is paid $10.25 per hour. Javier
earns $410 in commissions and is paid $12.50 per
hour. What will you find if you solve for x in the
equation 10.25x + 680 = 12.5x +410?
The earnings for both Cynthia and Javier are same for x hours.
What is commission?
When an employee completes a task, typically selling a certain volume of goods or services, they are compensated financially. Sales commissions are occasionally used by employers as incentives to boost employee productivity. It is possible to receive a commission in place of or in addition to a salary.
Given:
Cynthia earns $680 in commissions and is paid $10.25 per hour.
Javier earns $410 in commissions and is paid $12.50 per hour.
So, the equation is
10.25x + 680 = 12.5x + 410
To simplify this equation for x.
10.25x+ 680 =12.5x +410
680 ‐ 410 = 12.5x ‐ 10.25x
270 = 2.25x
x = 270/2.25
x = 120
If we plug x = 120 in both the values 10.25x + 680 and 12.5x + 410 then we will get the same values.
Hence, the earnings for both Cynthia and Javier are same for x hours.
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Please help find the value of x!!
Answer:31
Step-by-step explanation: solve it
There are more than 360 different breed of dog recognized worldwide. Which inequality repreent thi tatement?
x > 360
x < 360
x ≥ 360
x ≤ 360
Answer:
should be the first one, x > 360
Step-by-step explanation:
im sorry if its wrong :*(
What is the approximate perimeter of this triangle?
Answer:
Step-by-step explanation:
perimeter = hypotenuse + side a + side b
sin = opposite / hypotenuse
tan = opposite/adjacent
find the hypotenuse
let x = hypotenuse
sin(55 deg) = 56 / x
x * sin(55 deg) = 56
x = 56 / sin(55 deg) use a calculator
x ~ 68.36
find the side adjacent to 55 degrees
let x = adjacent leg
tan(55 deg) = 56 / x
x * tan(55 deg) = 56
x = 56 / tan(55 deg) use a calculator
x ~ 39.21
add them together
perimeter = 56 + 68.36 + 39.21
perimeter ~ 163.57 or 164
the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?
The probability that the next report will weigh less than 45 grams = 0.106
In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.
We need to find the probability that the next report will weigh less than 45 grams.
We have mean= 60 grams
Standard Deviation = 12 grams
First we convert 45 to z score.
45 converted to z score for given mean and standard deviation will be:
z = (45 - 60)/12
z = -1.25
So, from standard normal table a P-value:
P(x<45) = 0.10565
Therefore, the probability would be 0.10565
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Which of these represents the graph of x + 3y = 6
Answer:
PLEASE ADD A DANG PICTURE
Step-by-step explanation:
Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $264.00. On her second business trip she drove 200 miles in 3 days, and paid $165.00 for the rental. Find the daily fee, and find the mileage charge.
h(a)=5a²
What is h(6)?
Answer:
h(6) = 180
Step-by-step explanation:
h(a)=5a²
for a=6
h(6) = 5(6)²
h(6) = 5*36
h(6) = 180
Solve the system. Explain your answer using words, symbols, or both.
x+2y=8
x+y=2
Answer:
Using substitution method for to solve, X = -4 and Y = 6
Step-by-step explanation:
1) x+2y = 8
2) x+y = 2
solve 2)
x = 2-y
Then replaced it in 1)
(2-y) + 2y = 8
2 + y = 8
y = 6
then
x = 2 - 6
X = -4
Help please!!!!!!!!!!
Answer:
36
Step-by-step explanation:
4/9 x = 16
9/4 * 4/9 x = 16 * 9/4
x = 36
A company's minimum cost of $1000 occurs when operating for 16 hours per day. The cost of operating 8 hours per day would be $2600. Write a quadratic equation that models the company's costs.
The quadratic equation that models the company's costs is y = 25(x - 16)² + 1000
How to determine the quadratic equation that models the company's costs.From the question, we have the following parameters that can be used in our computation:
Minimum cost of $1000 at 16 hours
Operating cost of $2600 at 8 hours
A quadratic equation is represented as
y = a(x - h)² + k
The minimum point is the vertex
So, we have
(h, k) = (16, 1000)
Substitute (h, k) = (16, 1000) in y = a(x - h)² + k
y = a(x - 16)² + 1000
The cost of $2600 at 8 hours means
(x, y) = (8, 2600)
So, we have
2600 = a(8 - 16)² + 1000
Evaluate the difference
1600 = a(8 - 16)²
So, we have
64a = 1600
Divide by 64
a = 25
Substitute a = 25 in y = a(x - 16)² + 1000
y = 25(x - 16)² + 1000
Hence, the equation is y = 25(x - 16)² + 1000
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