Using a system of equations, it is found that there were 3 associates and 5 partners assigned to the case.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of associates.Variable y: number of partners.The firm assigned a total of 8 lawyers to the case, hence:
x + y = 8
x = 8 - y.
The firm was able to charge the client $6500 per day for these lawyers' services, hence, considering the costs:
500x + 1000y = 6500.
Since x = 8 - y, we have that:
500(8 - y) + 1000y = 6500.
500y = 2500
y = 5.
x = 8 - 5 = 3.
The firm assigned 3 associates and 5 partners to the case.
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What is the quotient?
1.242 ÷ 1.8 =
Answer: 0.69
Step-by-step explanation:
1.242 ÷ 1.8=
1.242/1.8=0.69
A boat is traveling at a constant rate through the water. if it takes 15 minutes to travel 2.7 miles, how many hours will it take for the boat to finish a 17.1 mile journey?
Answer:
6.3 hours
Step-by-step explanation:
all employees surveyed said that if they were in a state of information underload, they were dissatisfied.
Nearly 80% of those surveyed said they want to work for a company that values diversity, equity, and inclusion issues.
What is equity?
Value is utilized as capital raised by an organization, which is then used to buy resources, put resources into ventures, and asset tasks. A firm commonly can raise capital by giving obligation (as a credit or through bonds) or value (by selling stock). In finance, value is responsibility for that might have obligations or different liabilities joined to them. Value is estimated for the purpose of bookkeeping by taking away liabilities from the worth of the resources. For instance, on the off chance that somebody possesses a vehicle worth $24,000 and owes $10,000 on the credit used to purchase the vehicle, the distinction of $14,000 is value. Value can apply to a solitary resource, like a vehicle or house, or to a whole business. A business that requirements to fire up or grow its tasks can offer its value to raise cash that doesn't need to be reimbursed on a set timetable.
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What's the lcd of 1/3 and 3/9
Answer:
LCD = 9
Step-by-step explanation:
1/3 = 3/9
3/9 =3/9
I dont understand what i am supposed to do
Applying the alternate exterior angles theorem, the value of x = 10.
How to Apply the Alternate Exterior Angles Theorem?According to the alternate exterior angles theorem, the following alternate interior angles are congruent to each other:
m<JPM = m<NQK
Given the following:
m<JPM = 125°
m<NQK = (13x - 5)°
Substitute
125 = 13x - 5
125 + 5 = 13x
130 = 13x
Divide both sides by 13
130/13 = 13x/13
10 = x
x = 10
Therefore, applying the alternate exterior angles theorem, the value of x = 10.
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HELP 50 PTS AND BRAINLY!!!
Answer:
Last option
Step-by-step explanation:
→ Find the sum for how much he spent
[tex]\frac{2}{3} +\frac{1}{4} =\frac{11}{12}[/tex]
Answer:
C
Step-by-step explanation:
Which of the following could be a real-world description of 4x − 17?
$17 in addition to the cost of 4 hot dog combos
The cost of 17 people splitting 4 hot dog combos
$17 less than the cost of 4 hot dog combos
The cost of hot dog combos less a $17 coupon split by 4 people
The answer choice which could represent the real-world description of 4x - 17 is; $17 less than the cost of 4 hot dog combos.
What could be a real-world description of the expression?It follows from the task content that the real-world description of the expression; 4x -17 is to be identified.
On this note, if the cost of 1 hot dog is; x.
Hence, the cost of 4 hot dogs is; 4x.
Ultimately, the given expression represents; $17 less than the cost of 4 hot dog combos.
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Answer: C
Step-by-step explanation:
A car detailing shop charges $30 for materials, plus $50 per hour for labor to paint pinstripes on a car. Which function can be used to find the total cost C(h) to get pinstriping that requires h hours to complete?
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 50h + 30
How to create Cost Function?
We are given the following costs in the car detailing shop as follows;
Cost of Materials = $30
Cost per hour for labor = $50
Since the equation of a line in slope intercept form is; y = mx + c, then we can say that the equation here can also be expressed as;
C(h) = 30 + 50h
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 30 + 50h
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If 6 burgers cost $7.74, how many can you buy for $19.35? Pls show work and explain how you did it :)
Answer: 15 burgers
Step-by-step explanation:
7.74/6=$1.29 per burger
$19.35* 1 burger/$1.29=
19.35*1/1.29=
19.35/1.29=15 burgers
The sum of two numbers is 88. If one number is 4 more than half the other number, determine the two numbers by setting up a linear equation.
a.44
b.56
c.61.3
d.126
e.138
f.176
Need answer ASAP. Please no answer links. Will mark brainliest if you want.
The two numbers by setting up a linear equation are 32 and 56 respectively
Linear function and equationA linear equation is an equation that has a linear degree of 1. Let the 2 unknown number be x and y
If the sum of two numbers is 88, then;
x + y = 88
If one number is 4 more than half the other number, then
x = 1/2y + 4
Substitute equation 2 into 1
x + y = 88
(1/2y+4) + y = 88
1/2y+y + 4 -88 = 0
3/2y - 84 = 0
3/2y. = 84
3y = 2(84)
3y = 168
y = 56
Determine the value of x
x =88 - 56
x = 32
Hence the two numbers by setting up a linear equation are 32 and 56 respectively
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2. Select the numerical representation for the description.
Twenty-seven percent of three million:.
O27 x 3,000,000
O 0.27 x 3,000,000
O 0.27-3,000,000
O 0.27 +3,000,000
0.27 3,000,000
Answer:
27% of a 3m is 810,000
but here answer r is 0.27 3,000,000
Numerical representation of Twenty-seven percent of three million will be 0.27 x 3,000,000 .
The correct option is B.
Given, word form Twenty-seven percent of three million.
Conversion of word form into numerical form.
1 million = 1,000,000
Using unitary method,
Multiply both sides by 3.
1 million × 3 = 1,000,000 × 3
3 million = 3,000,000
Now 27% in terms of fraction can be written as :
27% = [tex]\frac{27}{100}[/tex]
= 0.27
Combining ''Twenty-seven percent of three million" :
Of in mathematics represent multiplication .
0.27 × 3000000
Thus the correct option is B .
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The table shows the results of an experiment in which three coins were tossed.
What is the experimental probability that at least two of the coins will be heads? The theoretical probability?
The experimental probability that at least two heads would be gotten is 11 / 25.
The theoretical probability that at least two heads would be gotten is 1/2.
What are the probabilities?Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability = number of times at least two heads would be gotten / total number of tosses
( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25
Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes
4 / 8 = 1/2
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Evaluate: 3a x 5w (Not simplified)
The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
What is the value of the expression otherwise termed it's simplified form as required that the expression be evaluated?It follows from the task content that the expression which is as given in the task content be evaluated, and hence, expressed in its simplified form.
Given;
3a × 5w
Since, the constants can be multiplied and their product determined, it follows that we have;
(3 × 5) (a × w)
And ultimately, we have the value of the expression to be; 15aw.
Therefore, The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
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Factor.
y²-9 please help me with this
Since both terms are perfect squares, factor using the difference of squares formula,
a2−b2=(a+b)(a−b) where a=y and b=3.
(y+3)(y−3)
a $5.62
b $7.42
At the grocery store, Ruby buys 3 packs of juice for $2.12 each, and 4 bags of popcorn for $3.50 each. What is the total amount that Ruby
spends on the juice and popcorn?
c) $18.98
Line
Guide
$20.36
Answer:
20.36 is the answer
2.12x3=6.36
3.50x4=14
14+6.36=20.36
Answer:
20.36
Step-by-step explanation:
1)3*2.12=6.36
2)4*3.50=14
3)6.36+14=20.36
the population standard deviation for the height of college baseball players is 3.0 inches. if we want to estimate 95% confidence interval for the population mean height of these players with a 0.68 margin of error, how many randomly selected players must be surveyed?
The number of players randomly selected is 381 and the standard deviation is 1.96.
What is the standard deviation?The standard deviation is a measurement of how much a group of values varies or is dispersed. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection. The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD. A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
[tex]Z(\alpha /2)=1.96[/tex]
Sample size = n = [tex][Z(\alpha /2 * \sigma/E) ]^{2}[/tex]
n = [1.96 * 3.0 / 0.95]²
n = 381.85
n ≈ 381
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what is the probability that a single card drawn from a standard deck of cards is either an 8 or a heart?
The probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
Probability of an event E denoted by P(E) is defined as (number of favorable outcomes )/( total number of outcomes).
For example : the probability of getting Head in single toss of an unbiased coin. P(H)=1/2.
According to the given question
Total number of cards in a standard deck of cards is 52.
There are 4 suit in a deck each having 13 card each.
number of 8 card in a deck = 4
Number of hearts in a deck = 13-1=12 (-1 because 8 of heart is counted before.)
number of favorable cases of getting either an 8 or a heart is 4+12=16.
The probability of getting either an 8 or a heart is [tex]\frac{16}{52} =\frac{4}{13}[/tex].
Therefore , the probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
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8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables (letters). use the sketch area if needed. combine the like terms and submit your answer. *always combine like terms in alphabetical order and write your constant term last!
When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
Given,
The expression =8+3a+7b-5+2a-7b
Rearrange the terms alphabetical order and combine the like terms
8+3a+7b-5+2a-7b =3a+2a+7b-7b+8-5
=(3+2)a+(7-7)b+(8-5)
=5a+0b+3
=5a+3
Hence, When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
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determine whether the statement describes a descriptive or inferential statistic. a survey of 1455 people revealed that 53% work a full-time job; therefore it can be assumed that 53% of the u.s. population works a full-time job.
The statement, "A survey of 1455 people revealed that 53% work a full-time job; therefore it can be assumed that 53% of the u.s. population works a full-time job" describes Inferential statistics.
What is inferential statistics?Inferential statistics is a sort of statistic that requires people to reach a conclusion based on some previously provided samples. In the statement above, we can see some statistics that have been previously stated that is followed by a conclusion.
The assumption that is made in the latter part of the statement is the reason why the statement can be referred to as inferential statistics.
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Please solve this simple order of operations question. Make sure to show your work. No links are allowed and answers with links will be reported! First person to answer will get brainliest ! Thank you.
[5−2² + (−3)]³ ÷ (-4)
Answer:
2
Step-by-step explanation:
First you do the 2² which is 4 then 5-4 is 1-3 is -2³ is -8/-4 is 2
what is 4 multiplied by 4
Answer:
4 × 4 is 16.
Multiplication:
Multiplication is the operation of increasing a value by another value the number of times the other value says to increase the first value.
e.g, 5 × 6 = 30
for how many different digits n is the 3 digit number 14n divisible by n, 14n refers to a three digit number with the unit digit of n
0, 1, 2, 4, 5, and 7.
So that would be 6 digits.
In mathematics, the only single symbol used to represent a number is a digit. For instance, there are two digits in the numbers 89: 8 and 9. As a result, in everyday life, digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, and 0 are employed to represent groups of numbers and perform mathematical operations. A positional numeral system uses a single sign, such as "2," or a set of symbols, such as "25," to represent numbers. The word "digit" derives from the fact that the ten fingers of the hands, or digit in Latin, corresponding to the ten symbols of the decimal system, which uses the base-10 numeral system.
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find the solutions to the equation in the interval 0 ≤ theta ≤ ????/2 . enter your answers as a comma-separated list. 2cos(4theta) − 1
The values of θ, i.e. the general solution of the given trigonometric equation that satisfy the given equation are: 5π/12, π/12.
What is the general solution of a trigonometric equation?The general solution of a trigonometric equation is a formula employing the integer n that provides all solutions.
Given:
EQuation: 2 cos( 4θ) - 1 = 0.Interval: 0 ≤ θ ≤ π/2TO find: Values of θ.
Finding:
In the given equation: 2 cos( 4θ) - 1 = 0,
=> cos (4θ) = 1/2
=> cos (4θ) = cos (π/3)
=> 4θ = 2nπ ± π/3
=> θ = nπ/2 ± π/12
For n = 0, θ = ± π/12
For n = 1, θ = π/2 ± π/12
Since θ ∈ [0, π/2], the possible values of θ = π/12, π/2 - π/12 = 5π/12.
Hence, The values of θ that satisfy the given equation are: 5π/12, π/12.
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The area of a closet is 100 sq feet. write the number in exponent form and word form.
For given number 100
the exponent form = 10²
the word form = One Hundred
For given question,
The area of a closet is 100 square feet.
We need to write the number in exponent form and word form.
First we write given number in exponent form
⇒ 100 = 10 × 10
⇒ 100 = 10²
So, the exponent form given number 100 is 10²
And the word form of given number is : One Hundred
Therefore, for given number 100
the exponent form = 10²
the word form = One Hundred
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Is the following conditional true?
If a number is a square root of an integer, then it is irrational.
Answer:
Step-by-step explanation:
The square root of an integer is either an irrational number or an integer. The latter is the case if and only if there is an integer which, when multiplied by itself, or squared, yields the number inside the symbol (the radicand) as the product. All square roots except perfect squares are irrational numbers. 3 is not a perfect square.
Use the number line to find pairs of equivalent fractions between 0 and 1
Answer:
4/8 and 3/6 are equivalent because they both equal 1/2.
Answer:
4/8 and 3/6
Step-by-step explanation:
0.5{3x + 4(3 + 2x)}
please simplify!!
Answer:
0,5(3x+12+8x)
0,5(11x+12)
5,5x+6
Answer:
5.5x + 6
Step-by-step explanation:
0.5{3x + 4(3 + 2x)}
Apply the distributive property, multiply 4 by 3 and 4 by 2x.
0.5(3x + 12 + 8x)
Add 3x and 8x
0.5(11x + 12)
Apply the distribdistributive proproperty again and multiply 0.5 by 11x and 0.5 by 12.
The product would be 5.5x + 6.
Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
5x+1/3 (3x-6)=10
Answer:
x=2Step-by-step explanation:
5x+1/3(3x−6)=10
Simplify both sides of the equation:5x+1/3(3x−6)=10
5x+(1/3)(3x)+(1/3)(−6)=10 (Distribute)
5x+x+−2=10
(5x+x)+(−2)=10 (Combine Like Terms)
6x+−2=10
6x−2=10
Add 2 to both sides:6x−2+2=10+2
6x=12
Divide both sides by 6:6x/6=12/6
x=2
Please help with problem 29
Answer:
Step-by-step explanation:
So, basically, the slope intercept form is y = mx + b
m is rise over run x is well x and b is where the original y is.
So 2x-3 is up two over one
And 1x-1 is up one over one
And take for example 2/3x + 5
That would be up two over three
Point P is located 2/5 of the distance from W to Z. Point W is located at (-5, -2) and point P is located at (1, 4). What are the coordinates of point Z?
The coordinates of point Z is (-5/7, 16/7)
Calculating the midpoint of a line using a ratioThe formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:
Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}
Substitute the coordinates and ratios to have;
Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}
Z(x, y) = {-10+5/7, -4+20/7}
Z(x, y) = (-5/7, 16/7)
Hence the coordinates of point Z is (-5/7, 16/7)
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