The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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I don't understand how to figure out the product:
Write 91 as the product of prime factors in ascending order
Then, work out the HCF of 91 and 130
91 as a product of its prime factors will be 7 and 13.
The highest common factor of 91 and 130 is 13.
How to calculate the factor?The process of factorization simony has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.
The factor of 91 include 1, 7, 13 and 91
The factor of 130 include 1, 2, 5, 10, 13 65, and 130.
The highest factor is 13.
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Your uncle is trying to decide between the purchase of a sports car or a SUV. The
sports car is cheaper to buy but costs more to insure. Specifically, the sports car
would cost $5000 plus $2500 each year for insurance, while the SUV would be
$8000 plus $800 per year to insure. After how many years would the amount
spent on each vehicle be the same?
The number of years it will take such that amount spent on each vehicle is the same will be 2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Suppose after x years the amount will be the same.
5000 + 2500x = 8000 + 800x
2500x - 800x = 8000 - 5000
1700x = 3000
x = 1.76
Since x must be a whole number so it will round up so x = 2.
Hence "The number of years it will take such that amount spent on each vehicle is the same will be 2".
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(1 point) how many strings of four decimal digits (note there are 10 possible digits and a string can be of the form 0014 eth., i., can start with zeros.) (a) end with an even digit? (can repeat digits.) 5000 (b) begin with an odd digit? (can repeat digits.) 5040
(a) 10⁴ strings of four digits which end with an even digit.
(b) 10⁵ strings of four digits which begin with an odd digit.
(a)There are 10 choices ranging from 0 to 1,2...9 for the first three digits of the string that ends in an even number and four possibilities ranging from 2,4,6,8, for the last digit.
According to the product rule there are 4000 strings that terminate in an odd number or 10 × 10 × 10 × 4.
(b) Also there are 10 choices ranging from 0 to 9 for the last three digits of the string that ends in an odd or even number and 5 possibilities ranging from 1,3,5,7,9 for the first digit .
According to the product rule there are 5000 strings that terminates in an even number or 10 × 10 × 10 × 5.
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how many different ways are there to seat five people around a circular table, where two seatings are considered to be the same if each person has the same neighbor to the left and the same neighbor to the right?
If the person has same neighbor to the left and right , Seating is considered same. By using circular permutation, the answer is 2.
What do you mean by permutation?A conceivable order or arrangement for a group of items, especially one among several alternatives.
What is the formula to calculate permutation?The formula for permutation is:
[tex]P(n,r)= \frac {n!}{(n-r)!}[/tex] (Permutation)
[tex]P(n)=(n-1)![/tex] (Circular permutation)
Total number of people=5
Since the orientation with same neighbor to left and right is considered same. We consider 3 people as 1 which represent a person with neighbors.
Total people used in circular permutation=3
P(3)= (3-1)!
=2!
=2.
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Angle 9 and angle 10 are corresponding angles formed by two parallel lines cut by transversal. The angles are also complimentary. Find angle 9
The measure of angle 9 is 45 degrees.
What is complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
Given:
Angle 9 and angle 10 are corresponding angles formed by two parallel lines cut by transversal.
The angles are also complimentary.
We have to find the measure of angle 9.
If <9 and <10 are corresponding, it means they are equal i.e <9 = <10
Since <9 and <10 are also complementary angles, their sum will be 90 degrees
<9+<10 = 90
<9 + <9 = 90
2m<9 = 90
m<2 = 90/2
m<2 = 45 degrees
Hence the measure of angle 9 is 45 degrees.
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what is s for the following function
Step-by-step explanation:
you just need to put the value for t into the equation and then solve for s.
t = 3s + 2
t = 11
11 = 3s + 2
3s = 11 - 2 = 9
s = 3
t = 17
17 = 3s + 2
3s = 17 - 2 = 15
s = 5
t = 23
23 = 3s + 2
3s = 23 - 2 = 21
s = 7
t = 29
29 = 3s + 2
3s = 29 - 2 = 27
s = 9
Determine the x and y intercept:
X -3 -2 -1 0 1
y 0 2 4 6 8
What is static electricity?
Build up of electrical charges on the surface of an object
Build up of light energy that causes electrical charges to move
The flow of electrical charges in a conductor
The movement of electrical charges through an insulator
Static electricity is an imbalance of electric charges within or on the surface of a material.
What is a charge? What is current?Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field.Electric charge can be positive or negative. Like charges repel each other and unlike charges attract each otherRate of flow of charge per unit time is called current.We have static electricity.
Static electricity is an imbalance of electric charges within or on the surface of a material or between materials. The charge remains until it is able to move away by means of an electric current or electrical discharge.
Therefore, Static electricity is an imbalance of electric charges within or on the surface of a material.
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a card is selected from a standard deck and replaced. this experiment is repeated a total of five times. find the probability of selecting exactly three clubs. a. identify a trial, a success, and a failure. b. identify n,p,q,and x. c. use the binomial probability formula.
The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.
What is the binomial probability formula?The binomial probability formula is
P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = [tex]\frac{n!}{(n-x)!x!} p^xq^{(n-x)}[/tex]
Where n is the number of trials, p i is the probability of success, and q is the probability of failure.
And q = 1 - p
Calculation:It is given that, a card is selected from a standard deck and replaced.
This experiment has repeated a total of five times. i.e., trials n = 5
So, the probability of success is p = 1/4 = 0.25
(Since one card is to be selected from the five trials where each time the card is replaced)
Then, the probability of failure is q = 1 - 0.25 = 0.75
And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.
Then, using the binomial probability formula, we get
P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878
On rounding off, we get the required probability as 0.088.
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Write a polynomial function that meets the stated condition.
The zeros are -2/3 and , and the constant term of the polynomial is -10.
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The zeros are -2/3. Then the factor of the polynomial is given as,
x = - 2/3
3x = - 2
3x + 2 = 0
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be given as,
p(x) = 3x + 2 - 10
p(x) = 3x - 8
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
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DOUBLE POINTS!!! Please help!
answer
x=-10
x=0
Step-by-step explanation:
x(x+10) =0
apply zero product property
sorry if this is a straight forward answer
Answer:
The first solution is -10 and the second solution is 0
Step-by-step explanation:
The question is x * (x+10) = 0
When the product of factors equals 0, at least one factor is 0:
x = 0
x+10 = 0 which can be simplified to x = -10 by subtracting 10 from both sides. Thus, the two solutions to x * (x+10) = 0 is -10 and 0.
if the radius is 40 what is the circumference
Answer:
Step-by-step explanation:
Solve using substitution x=-3 -4x-y=10
A commuter travels to work using a city bus. The function f(t)=−600t+12,000 represents the distance remaining, in meters, after t minutes of riding the bus.
What does −600 represent in the function f(t)?
Responses
the slope of the function and the change in distance remaining, in meters per minute, of riding the bus
the slope of the function and the change in distance remaining, in meters per minute, of riding the bus
the slope of the function and the initial number of meters remaining when t=0
the slope of the function and the initial number of meters remaining when t = 0
the y-intercept of the function and the change in distance remaining, in meters per minute, of riding the bus
the y -intercept of the function and the change in distance remaining, in meters per minute, of riding the bus
the y-intercept of the function and the initial number of meters remaining when t=0
the y -intercept of the function and the initial number of meters remaining when t = 0
The interpretation of -600 is (a) the slope of the function and the change in distance remaining, in meters per minute, of riding the bus
How to interpret -600 in the equation?From the question, we have the following parameters that can be used in our computation:
f(t) = -600t + 12000
A linear equation is represented as
y = mx + c
Where
Slope = m
When the equations are compared, we have
m = -600
This means that
Slope = -600
So, the interpretation of -600 is the slope
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data shows that the united states has less intergenerational mobility than germany. that means that:
The data shows that United States has less intergenerational mobility than Germany this data means that the success of the children of United States depends more on the parents income status in comparison to Germany.
Intergeneration mobility is the extent to which the outcomes of the doings of an individual are different in comparison to his or her parents. This basically means the extent to which an individual is gaining something by his own potential.
According to the data United States has less intergeneration mobility in comparison to the intergenerational mobility of Germany.
From this data that outcomes of a children born in United States depends highly on the parents economic and financial status than German kids.
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A group of friends wants to go to the amusement park. They have no more than $280
to spend on parking and admission. Parking is $20, and tickets cost $40 per person,
including tax. Write and solve an inequality which can be used to determine a, the
number of people who can go to the amusement park.
[tex]\boxed{20+40a \leq 280}\\\\1+2a \leq 14\\\\2a \leq 13\\\\a\leq \frac{13}{2}[/tex]
However, since there must be a whole number of people, this rounds down to [tex]\boxed{a \leq 6}[/tex]
(d) Use function notation to write g in terms of f.
1. g(x) = (x − 10)2
f(x)= x2
answer: g(x)= f(____)
2. g(x)= -x3-2
f(x)= x3
answer: g(x)= -f(____) + (____)
3. g(x)= -(x+6)2+2
f(x)= x2
answer: g(x)= -f(____) + (____)
4. g(x) = (x + 2)3 − 8
f(x)= x2
answer: g(x)= f(____) + (____)
5. g(x) = 8 − |x + 4|
f(x)= |x|
answer: g(x)= ____ - f(____)
6. g(x) = |−x + 5| + 7
f(x)= |x|
answer: g(x)= f(____) + (____)
7.
f(x)= √x
answer: g(x)= f(____) + (____)
The value of g in terms of f is:
[tex]x^{4} -20x^{2} +100[/tex]
[tex]x^{9} -2[/tex]
[tex]-x^{4} -12x^{2} -34[/tex]
[tex]8-||X|+4|[/tex]
[tex]|-|x|+5|+7[/tex]
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
Finding g in terms of f, given:
g(x)=[tex]x-10^{2}[/tex],f(x)= [tex]x^{2}[/tex]
g(x)=g(f(x))
f(x)= [tex]x^{2}[/tex] =g( [tex]x^{2}[/tex])
g( [tex]x^{2}[/tex]): [tex](x^{2} -10)^{2}[/tex]
Expanding [tex](x^{2} -10)^{2}[/tex] : [tex]x^{4} -20x^{2} +100[/tex]
Finding g in terms of f, given:
g(x)=[tex]-x^{3} -2[/tex],f(x)= [tex]x^{3}[/tex]
g(x)=g(f(x))
f(x)= [tex]x^{3}[/tex] =g( [tex]x^{3}[/tex])
g( [tex]x^{3}[/tex]): [tex]x^{9} -2[/tex]
Finding g in terms of f, given:
g(x)=[tex]-(x-6)^{2} +2[/tex] ,f(x)= [tex]x^{2}[/tex]
g(x)=g(f(x))
f(x)= [tex]x^{2}[/tex] =g( [tex]x^{2}[/tex])
g( [tex]x^{2}[/tex]): [tex]-x^{4} -12x^{2} -34[/tex]
Finding g in terms of f, given:
g(x)=[tex]8-|x+4|[/tex] ,f(x)= [tex]|x|[/tex]
g(x)=g(f(x))
f(x)= [tex]|x|[/tex] =g( [tex]|x|[/tex] )
g( [tex]|x|[/tex] ): [tex]8-||X|+4|[/tex]
Finding g in terms of f, given:
g(x)=[tex]|-x+5|[/tex] ,f(x)= [tex]|x|[/tex]
g(x)=g(f(x))
f(x)= [tex]|x|[/tex] =g( [tex]|x|[/tex] )
g( [tex]|x|[/tex] ): [tex]|-|x|+5|+7[/tex]
[tex]|-|x|+5|+7[/tex]
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Is y=4+x a proportional relationship??
Hence, [tex]y=4+x[/tex] is a proportional relationship.
What is the proportional?
Proportional or proportion meaning in math means equality between two ratios. In the mathematical equation [tex]\frac{a}{b}=\frac{c}{d}[/tex], where [tex]a[/tex] and [tex]b[/tex] are in a similar proportion as [tex]c[/tex] and [tex]d[/tex].
A proportion is essentially established for solving a word problem in which one of its four quantities is unknown.
Here given that,
We have to check [tex]y=4+x[/tex] is a proportional relationship or not.
So, the given equation is
[tex]y=4+x[/tex]
Here, [tex]4[/tex] is constant.
So, [tex]y=4+x[/tex] is a proportional relationship.
Hence, [tex]y=4+x[/tex] is a proportional relationship.
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a group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths, stones that form in the colon of horses, and diet. they decided to conduct a survey of feeding practices of horses in the hospital's state. they created a survey questionnaire and decided to administer it to the owners of every fifth horse being treated at the hospital. the sample is a:
Fron the given question, we can say that systematic sample because not all sample are possible.
What is Systematic sampling?Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.
[tex]Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.[/tex]
Further,
Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.
If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.
If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.
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6. In July, the price of a gallon of gasoline rose 12%. In August it fell 15% of its final July price, ending
the month at $1.19. What was its price at the beginning of July?
According to the question,
Given data in the question,
In July, the price of a gallon of gasoline rose=12%
In august, it fell 15% of its final July price,
Ending the month at 1.19 rupees
Let us consider,
x is the original price at the beginning of July,
then the price of gasoline rose is 112%
=100+2
=112%
=112/100
=1.12
In august it fells 15%=100-15%
=.85%
With the help of given data
the original price is---- x
(1.12) × (.85) x = 2.29
find the value of x
x = 2.29/0.952
x=2.41
x=2.41 was its price at the beginning of July.
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Help please
Multiply.
-2w(-5-w)
Answer:
[tex]10w + 2w^{2}[/tex]
Step-by-step explanation:
To solve this, we have to apply the distributive property and simplify:
(-2w x -5) + (-2w x -w)
[tex]10w + 2w^{2}[/tex]
Answer:
[tex]10w + 2w {}^{2} [/tex]
Help me please! I don’t understand
Answer: Yes, they receive more than $82 for their job
Step-by-step explanation:
First, take 70 times 0.05% = $3.50
Then add them to equal $73.50 is their charge for the job!
Now it says that the homeowner tip 15%
So take 73.50 times 0.15% = $11.03
Then add 73.50 with 11.03 = $84.53
Yes, they receive more than $82 for their job
Evaluate 9.1p + 8.9r when p = 6 and r =7.
Answer:
116.9
Step-by-step explanation:
9.1(6) + 8.9(7)
54.6+62.3
116.9
Please Help! Three times the quantity of a number increased by 7 is equal to the same number decreased by 15
The value of the number will be;
⇒ x = - 11
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''Three times the quantity of a number increased by 7 is equal to the same number decreased by 15''
Now,
Let the quantity of a number = x
So, We can formulate;
⇒ 3x + 7 = x - 15
Solve for x as;
⇒ 3x - x = - 15 - 7
⇒ 2x = - 22
⇒ x = - 11
Thus, The value of the number will be;
⇒ x = - 11
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Please answer both what angle relationship it is and what x equals
By analyzing the geometric system presented in the figure, the angle x has a measure of 56°.
What is the measure of the missing angle within a pair of angles?
In this question we find a representation of pair of angles, that is, a geometric system with two adjacent angles. The sum of the measures of the two angles equals 98° and one of the angles has a measure of 42°:
42° + x = 98°
x = 98° - 42°
x = 56°
The missing angle x has a measure of 56°.
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calls to the help line of a large computer distributor follow a poisson distribution with a mean of 23 calls per minute. (a) what is the mean time until the one-hundredth call? minutes (round your answer to 2 decimal places.) (b) what is the mean time between call numbers 50 and 80? minutes (round your answer to 2 decimal places.) (c) what is the probability that three or more calls occur withing 15 seconds? (round your answer to 3 decimal places.)
Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754
What is poisson distribution?The Poisson distribution, used in probability theory and statistics, is a discrete probability distribution that expresses the likelihood that a specific number of events will take place within a predetermined window of time or space, provided that they do so at a known constant mean rate and regardless of the interval since the last event.
Here,
Thus, calls occur according to a poisson process with λ=23 calls per minute
a)X is the time until the one-hundredth call , X has Erlang distribution with rate of 23 and r =100
E(X)=r/ λ = 100/23 =4.35
b)The expected time between call numbers 50 and 80 is the same as the expected time until the 30th call this is Erlang distribution with rate of 23 and r =30
E(X)=r/ λ =30/23=1.30
c)P(N≥3) λ=23, x=1/4 ,λx=5
1-P(N≤2) = 1- ∑ [tex]\frac{e^{-5}-5^{k}}{k!}[/tex](from k=0 to 2 )=0.754
Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754
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a survey was taken of a random sampling of residents of new york city and los angeles to compare how many of them own a car. a 4-column table with 3 rows. the first column has no label with entries l a residents, n y c residents, total. the second column is labeled own a car with entries 3,251; 1,478, 4,729. the third column is labeled do not own a car with entries 869; 6,182; 7,051. the fourth column is labeled total with entries 4,120; 7,660; 11,780. which statement about the two-way frequency table is true?
The true statement is;
There is a greater percentage of Los Angeles residents who own a car than New York City residents who do
Given,
Following is the presentation of the values:
The number of residents in Los Angeles own a car = 3251
The number of residents in New York City own a car = 1478
Total residents who own a car = 4729
Los Angeles residents who do not own a car = 869
New York City residents who do not own a car = 6182
Total residents who do not own a car = 7051
Total Los Angeles residents sampled = 4120
Total New York City residents sampled = 7660
Total residents of both cities sampled = 11780
Here,
Percentage of Los Angeles residents who own a car = (3251/4120)×100 = 78.9%
Percentage of New York City residents who own a car = (1478/7660)×100 = 19.3%
Then,
The total number of people in the poll who own a car = 4729
Therefore,
The correct option is that there is a greater percentage of Los Angeles residents who own a car than New York City residents who do.
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Answer: B
Step-by-step explanation:
Solve the following system of equations graphically on the set of axes below. y=-3x - 6 x - 4y = -28
The solution to the given system of equations is;
x = -4 and y = 6
How to solve a set of equations graphically?We are given the simultaneous equations as;
y = -3x - 6 ------(1)
x - 4y = -28 ------(2)
For eq 1, we can get the coordinates as;
When x = -2, y = -3(-2) - 6 = 0
When x = -1, y = -3(-1) - 6 = -3
When x = 0, y = -3(0) - 6 = -6
When x = 1, y = -3(1) - 6 = -9
When x = 2, y = -3(2) - 6 = -12
For eq 2, we have;
When x = -2, y = (-2 + 28)/4 = 26/4
When x = -1, y = (-1 + 28)/4 = 27/4
When x = 0, y = (0 + 28)/4 = 7
When x = 1, y = (1 + 28)/4 = 29/4
When x = 2, y = (2 + 28)/4 = 7.5
From the graph attached, the solution is (-4, 6)
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A toy store received a shipment of stuffed animals. The store
displayed 2/5 of the stuffed animals at the back of the store. A display with 3/8 of the animals was at the front of the store. The rest of the stuffed animals were stored in a storage area. What fraction of
the stuffed animals was stored in the storage area?
Answer:
C) 9/40
Step-by-step explanation:
1 - [tex]\frac{2}{5}[/tex] - [tex]\frac{3}{8}[/tex] Make equivalent fractions with 40 as the denominator
[tex]\frac{2}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{16}{40}[/tex] Another name for [tex]\frac{8}{8}[/tex] is one. This is how we can make equivalent fractions.
[tex]\frac{3}{8}[/tex] x [tex]\frac{5}{5}[/tex] = [tex]\frac{15}{40}[/tex]
1 can also be written [tex]\frac{40}{40}[/tex]
[tex]\frac{40}{40}[/tex] - [tex]\frac{16}{40}[/tex] - [tex]\frac{15}{40}[/tex] = [tex]\frac{9}{40}[/tex]
Write the equation of the line perpendicular to y=-3x-1 that passes through the point (3,4)
The equation of the line perpendicular to y=-3x-1 that passes through the point (3,4) is y = (1/3)x + 3.
What do you mean by equation of line?
The slope of the line and a point on the line can be used to create the equation of a line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.
The slope of the line given in the question is: -3,
The slope of perpendicular line is negative reciprocal of the slope of other line,
So,
The slope of perpendicular line is: 1/3.
The equation of the line is generally in the form:
y = mx + c
So, the equation of line becomes:
y = (1/3)x + c
We have given that the line passes through the point (3,4).
Putting the values of x and y in the above equation to get the value of c.
4 = (1/3)(3) + c
c = 3
Putting the value of c in the equation,
y = (1/3)x + 3
This is the required equation.
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Answer:
(-3,-4) and (3,4).
Step-by-step explanation:
