(i) The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.
(ii) This equation has infinite number of solutions and it is an identity.
(iii) This equation has no solutions and it is a contradiction.
What is identity and contradiction?
An identity is an equation that can be solved using any integer that can replace the variable in the equation in a meaningful way. A conditional equation is one that is met by some numbers but not by others, such as 2x = 4. A contradiction is an equation, such as x = x + 1, that cannot be solved.
We know that,
An equation having infinitely many solutions is called an identity equation.
An equation that having no solution is called a contradiction.
(i) 6x + 4x - 6 + 24 + 9x
Combining like terms
x = 30
Therefore, The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.
(ii) 25 - 4x = 15 - 3x +10 - x
Combining like terms
0 = 0
It means, The equation is true for all values of x.
Therefore, This equation has infinite number of solutions and it is an identity.
(iii) 4x + 8 = 2x + 7 + 2x - 20
Combining like terms
8 = -13
It means, The equation is not true for any value of x.
Therefore, This equation has no solutions and it is a contradiction.
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The cost of 15 books is $33.75. Find the cost of 12 such books?
Answer:$27
Step-by-step explanation:
$33.75/15 = $2.25 per book
12 books x $2.25/book = $27
Please help, thanks in advance!
Answer: 114
Step-by-step explanation:
firstly, convert meters to centimeters:
2.5m * 100cm in a meter = 250 cm
let the length of the first shelf equal x:
250 = x + (2x + 18) + (x - 12) + (x + 4)
combine like terms:
250 = 5x + ( 18 - 12 + 4) = 5x +10
subtract 10 from both sides:
240 = 5x, then solve for x
240/5 = x
x = 48 cm
the length of the second shelf was 2x + 18, so plug in 48 for x:
2(48) + 18 = 114
Answer:
114 [cm].
Step-by-step explanation:
1) if the length of the 1st shelf is 'x', then
2) the length of the 2d shelf is '2x+18', the 3d shelf is 'x-12' and the 4th shelf is 'x+4';
3) the sum of the all 4 shelves is 250 [cm], then it is possible to make up the equation:
x+(2x+18)+(x-12)+(x+4)=250;
4) the root of the equation above is x=48, then
5) the required length of the 2d shelf is 2*48+18=114 [cm].
The following table provides a probability distribution for the random variable .
2 0.10
5 0.30
7 0.40
9 0.20
a. Compute (to 1 decimal).
6.3
b. Compute and (to 2 decimals).
3.45 incorrect
1.57 incorrect
Considering the discrete probability distribution, it is found that:
a) The mean is of: 6.3
b)
The variance is of: 4.01.The standard deviation is of: 2.What are the statistical measures for the discrete probability distribution?The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:
E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.
The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:
Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.
The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:
S(X) = sqrt(4.01) = 2.
Missing InformationWe have that:
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An bucket starts with 872 gallons of water and is emptying at a rate of 19 gallons per hour. If I know that the bucket has 8 gallons of water, how long has it been emptying?
Answer:
45.47368421 (round as much as you need)
Step-by-step explanation:
We can model the equation using G(h) = -19h + 872, where -19 is the rate at which the bucket is emptying and 872 is the amount of gallons the bucket starts with.
Since gallons is the output, we would have 8 = -19h + 872 and we simply need to solve for h
[tex](8 = -19h+872)-872\\\frac{(-864=-19h)}{-19} \\h=45.47368421[/tex]
Suppose that the functions and are defined for all real numbers as follows.
Write the expressions for and and evaluate .
The expression we get from the given functions f and g defined for all real numbers x.
(f+g)(x)=4x+1
(f-g)(x)=2x+11
(f.g)(3)=-30
Given that,
All real numbers x are defined by the functions f and g.
f(x)=3x+6
g(x)=x-5
We have to find the expression
(f+g)(x), (f-g)(x) and (f.g)(3)
Take the functions,
f(x)=3x+6
g(x)=x-5
Now, First
(f+g)(x)
f(x)+g(x) (Substitute in the place of f and g functions)
Which is
3x+6+x-5
4x+1
(f+g)(x)=4x+1
Now, second
(f-g)(x)
f(x)-g(x)
Which is
3x+6-(x-5)
3x+6-x+5
2x+11
(f-g)(x)=2x+11
Now, third
(f.g)(3)
f(3)×g(3)
Which is
(3(3)+6)×((3)-5)
(9+6)×(3-5)
15×-2
-30
(f.g)(3)=-30
Therefore, The expression we get from the given functions f and g defined for all real numbers x.
(f+g)(x)=4x+1
(f-g)(x)=2x+11
(f.g)(3)=-30
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Write an equation for a line parallel to y=-4x+3 and passing through the point (4, -20)
The equation of the line is y = -4x -4.
We need to calculate the line which is parallel to y = -4x +3 and passes through the point (4, -20)
The given equation is y = -4x +3
Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation is -4.
Now, When two lines are parallel to each other, their slopes are equal.
So, the slope of the required equation is -4.
Now, the equation of the line which passes through the points, [tex](x_{1} ,y_{1} )[/tex] and has slope m, is given by
[tex]y - y_{1} = m(x-x_{1} )[/tex]
Putting the values in the general equation, we get,
y - (-20) = -4(x - 4 )
y + 20 = -4x +16
y +4x = 16 -20 = -4
The equation of the line is y = -4x -4.
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10.
12.
(5x + 3)°
8x°
/(15x-7)°
Answer:
sada
Step-by-step explanation:
Please Add A Picture
when potatoes are peeled do you lose more peel when you use big potatoes or small potatoes
Answer:
depends on how you peel it
Step-by-step explanation:
if you peel it with one quick peel, you will have only one
if you do it with 2, you will have 2 peels an so on
The amount of peels will be greater in the bigger potato as compared to the smaller potato.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given data in the question,
There are two potatoes, a small one and a bigger one.
If you peel the bigger one, because of the bigger surface area, you will get more peels as compared to the smaller potato because the surface are is small, and you will get less number of peels.
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The 23 members of the westview journalism club are trying to raise at least 2,100 to buy new publishing desgin software. The members have already raised 1180. How much should each student still raise, on average, to meet the goal?
PLEASEEEE
The amount that each student will have to raise on average in order to meet the goal would be $40
How to find the amount to raise?First, find the remaining amount that the members of the Westview Journalism Club are trying to raise:
= Amount to raise - Amount already raised
= 2, 100 - 1, 180
= $920
The amount that each student in the club will have to raise on average can be found as:
= Amount remaining to be raised / Number of students in the Westview Journalism Club
= 920 / 23
= $40
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0/1
At the carnival, there is a game with 600 ducks. If 75% of the ducks have stars on the
bottom, how many ducks have stars? Make sure to label your answer in ducks
Answer:
450 ducks
Step-by-step explanation:
75% can be rewritten as 75/100
75/100 of 600 can be rewritten as 75/100 * 600
Solve 75/100 = 0.75
0.75 * 600 = 450
please help!! will mark brainlyist!!
Answer:
1. 4√5
2. 3√5
3. √149
4. √58
Step-by-step explanation:
The Pythagorean theorem states "a^2 + b^2 = c^2", where "a" and "b" are the legs, while "c" is the hypotenuse.
Knowing this, we can substitute each variable with given values on the triangles
1. "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"
4^2 + 8^2 = c^2
16 + 64 = c^2
80 = c^2
√80 = c
4√5 = c
2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"
6^2 + 3^2= c^2
36 + 9 = c^2
45 = c^2
√45 = c
3√5 = c
3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"
7^2 + 10^2 = c^2
49 + 100 = c^2
149 = c^2
√149 = c
4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
√58 = c
Tommy bounces a basketball 25 times in 45 seconds, At that rate, approximately how many
times will pat bounce the ball in 405 seconds?
Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.
What is the unitary method's formula?The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value. However, this approach is useful for determining the value of a unit from the value of a multiple, and hence the value of a multiple.Given: In 45 seconds, Tommy bounces a basketball 25 times.
Number of times he will pat bounce the ball in 405 seconds will be given as follows:
= (405 × 25)/45
=225
Therefore, Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.
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The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 24x
C(x) = 17x + 161
By calculating profit function to break even, the company needs to produce 23 units.
What is meant by profit function?The amount received when a good or service is sold for a price is referred to as revenue. The cost of a product or service is the amount spent on its sale. Profit is defined as the difference between revenue and costs. A profit function is a relationship that shows the difference between the cost and revenue functions. The graph of a profit function can show the best combination of revenue and costs to produce the most profit. This is known as optimization.
Profit is defined as revenue less costs. This means that there is a profit function, P(x).
P(x) = R(x) - C(x)
Breaking even is the point at which revenue begins to exceed costs. It is thus the point at which P(x) = 0. Because these are all linear functions, you know that the business will be profitable after that point.
P(x) = 0
R(x) - C(x) = 0
R(x) = 24x
C(x) = 17x + 161
From the above equation,
R(x)=C(x)
24x=17x+161
7x=161
x=161/7
x=23
For the company to break even, 23 units must be produced.
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(-9,-4); y=-3x+3
Write an equation for the line in slope-intercept form.
You have $4,500 on a credit card that charges a 15% interest rate. If you want to pay off the credit
card in 3 years, how much will you need to pay each month?
Which of these is a factor in this expression
Make the subject of
9x = u
Making the subject as x, the expression is x = u/9
The given equation is
9x = u
It can be written as
u = 9x
We need to make x as the subject in the given expression
9x = u
u = 9x
here u is the subject
9x = u
x = u/9
Therefore, making the subject as x, the expression is x = u/9
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Find the value of x ( please help die today!)
Answer:tell me the math soulation first
Step-by-step explanation:
The probability that aperson living in a certaincity owns a dog is estimated to be 0.3. Find the probabilitythat the tenth person randomly interviewed inthat city is the fifth one to own a dog.
The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051
Given,
Consider the interview of a person is a trial.
Lets consider it success if a person owns a dog and consequently , a person without a dog will be a failure.'
Let the random variable X represent the number of persons to be interviewed to get 5 dog owner: in other words, to get 5 successors.
Probability of a success in each trial is p = 0.3. Therefore probability of a failure in each trial is q = 1 - p = 0.7 .
Because trials are independent. X has a negative binomial distribution with parameters k = 5, p = 0.3
P(X =x ) = b(x: k, p) = [tex][(x-1)(k-1)] p^kq^r^-^k[/tex]
where, x = k , k + 1 , k + 2......(1)
Now, Lets find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog
Using equation (1), we get:
P(X = 10) = b(10: 5, 0.3)
= [(10-1) (5 - 1)][tex](0.3)^5(0.7)^1^0^-^5[/tex]
= [(9)(4)] [tex](0.3)^5(0.7)^1^0^-^5[/tex]
= 0.05146
Hence, The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051
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A fitted linear regression equation is y = 6-2x. If × - 3 and the corresponding observed value of y = 2, the residual at this observation is:
The value of the residual is 2.
We are given a fitted linear regression equation. The equation is given below.
ŷ = 6 - 2x
The x-value for the data points is 3, and the corresponding y-value is 2. We have to find the value of the residual.
We will substitute the given values in the equation of the regression line.
ŷ = 6 - 2x
ŷ = 6 - 2(3)
ŷ = 6 - 6
ŷ = 0
Thus, the predicted value of y in the given regression equation is 0. The actual value of y is 2. The residual is the difference between the actual and predicted values of y. Let the residual be denoted by the variable "r".
r = y - ŷ
r = 2 - 0
r = 2
Hence, the residual is 2.
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An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set an
acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a
mean repair time of 74 minutes with a standard deviation of 4.0 minutes and the other firm had a mean repair time of 72 minutes with a
standard deviation of 5.1 minutes. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Firm Cpk
1 ___
2 ___
Which firm would you choose?
Firm 1
Firm 2
None
The best firm for the Appliance manufacturer for the repair work is Firm 2 .
In the question ,
it is given that ,
An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .
The acceptable range of the repair time is 50 minutes to 90 minutes.
the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .
the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .
the range is calculated using the formula
Range = Mean ± Standard Deviation
So , for firm 1 ,
the Range = 74 ± 4
= 74 [tex]+[/tex] 4 and 74 - 4
= 78 and 70
the range for firm 2 is
= 72 ± 5.1
= 72 [tex]+[/tex] 5.1 and 72 - 5.1
= 7.1 and 66.9
The second company has a lower range and it should be preferred .
Therefore , The best firm for the Appliance manufacturer for the repair work is Firm 2 .
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Which number line represents the solution set for the given inequality? X + 1<_ -3 Or -4x < _
-8
Answer:
B
Step-by-step explanation:
OR means that they don't overlap and based on the answer you have in you know how to solve the innequality.
A classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m
a) how many boards are needed altogether
b) How many of them will be cut
c)find the total cost of each board costs #700
There will be 319 boards be required
and the total cost be $223,720.
Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.
Now, we have to find the number of boards needed altogether
So, the area of the ceiling is
Area = 6.8×4.7
Area = 319.6 m²
Now, the area of the board is
Area = 1 m²
So, 319 boards will be required to cover the ceiling.
Now, if one board costs $700 then,
the total cost be
= 700×319.6
= $223,720
Hence, There will be 319 boards be required
and the total cost be $223,720.
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sophie went to the lake with her family first they spent 1 1/4 hours fishing then they spent twice as much time swimming how much time did they spend swimming
Answer:
They spent a total of 1 and 1/2 hours swimming.
Step-by-step explanation:
It is because 1 1/4 plus 1 1/4 equals 1 2/4 which mean 2/4=1/2 so in total they spent 1 1/2 hours swimming
How do I simplify this expression
Given a standard deck of playing cards, what is the probability of drawing each hand:
2 diamonds
1 diamond and 1 heart
Explain why the more likely outcome, above, is more likely
The probability of drawing 2 Diamonds is 1/17.
The probability of drawing 1 diamond and 1 heart is 13/204.
How to find probability for a deck of cards?
In total there are 52 cards in a deck.these 52 cards are divided in 4 suits each having 13 card values.The 4 suits are: Clubs, Spades, Diamonds and Hearts.13 card values are: 2-10, King, Queen, Jack and an AceKing, Queen and Jack are called Face cards.For finding probability of chosen cards to cases arise: 1. With replacement of the drawn card; 2. Without replacement of the drawn cardAccording to the given question:
Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.
After the first card is drawn, there are just 12 diamonds left.
So, the probability of drawing the diamond now is 12/51.
The total probability is the product of two probabilities
So, P = 13/52 x 12/51 = 1/4 x 4/17
P = 1/17 ≈ 0.058
So the probability of drawing 2 Diamonds is 1/17.
Similarly, we know probability of getting a diamond in first is 13/52.
Also the probability of drawing a heart from 51 cards is 13/51.
The total probability P = 13/52 x 13/51
P = 1/4 x 13/51
P = 13/204 ≈ 0.063
So the probability of drawing 1 diamond and 1 heart is 13/204.
More likely outcome is the one whose probability is closer to unity. Since 13/204 > 1/17 that is 0.063 > 0.058 therefore drawing a heart and a diamond is a more likely outcome.
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Which of the following choices is the y-intercept of the equation -3x - 2y = 10?
3
-3
5
-5
Susie is visiting Germany from the U.S. One day she stopped by a market and found a stall selling tomatoes for 1.74 euro per kilogram. If 1 euro was worth 1.09
dollars that day, how much did the tomatoes cost in dollars per pound?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of
the equation.
The cost of the tomatoes, in dollars per pound, using proportions, is of:
$0.86 per lb.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.
In this problem, the costs is obtained as follows:
Cost: 1.74 euros per kilogram.Exchange ratio: 1 euro = 1.09 dollars.Hence the cost in dollars per kg of the tomatoes is obtained as follows:
1.74 x 1.09 = $1.8966 per kg.
The relationship between kg and pounds is given as follows:
1 kg = 2.20 lb.
Hence the cost is written as follows:
$1.8966 per 2.20 lb.
The cost per pound of the tomatoes is of:
1.8966/2.20 = $0.86 per lb.
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Select all statements that are true about the graph of h (x) = –3 |x – 1| + 4.
A. Its vertex is at (–1, 4).
B. Its vertex is at (1, 4).
C. Its line of symmetry is x = –1.
D. Its line of symmetry is x = 1.
E. It crosses the y-axis at (0, 1).
F. It crosses the y-axis at (0, 4).
The statements that are true according to the equation h (x) = –3 |x – 1| + 4. are
B. Its vertex is at (1, 4)D. Its line of symmetry is x = 1E. It crosses the y-axis at (0, 1)How to find the functions as requiredThe graph of the described function is attached
The vertex is marked (1, 4) in the graph
The y intercept is marked (0, 1) in the graph
Also from the equation, the y intercept is solved by
h (x) = –3 |x – 1| + 4
plugging the value of x
h (x) = –3 |0 – 1| + 4
h (x) = –3 |– 1| + 4
removing the modulus sign
h (x) = –3 * 1 + 4
h (x) = –3 + 4
h (x) = 1
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A right triangle has a leg length of square root of 6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle. 3 36 square root of 39 square root of 43
Answer:
√43
Step-by-step explanation:
Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.
a = √6 and c = 49
√6^2 + b^2 = 49
6 + b^2 = 49
b^2 = 43
b = √43
Answer:
The square root of 43
Step-by-step explanation:
I did this in class the other day