If R is a field, then: < x >= R[x] This option None of choices This option is not prime This option is maximal This option
Answers
The statement "< x >= R[x]" is false.
To understand why this is false, let's break it down. In the given statement, R is assumed to be a field, which means that it is a commutative ring where every nonzero element has a multiplicative inverse. In a field, every nonzero element is a unit, meaning it has a multiplicative inverse.
Now, let's consider the ideal generated by 'x' in R[x], which consists of all the polynomials in R[x] that can be expressed as multiples of 'x'. In other words, it is the set {a * x | a ∈ R[x]}.
If R is a field, then every nonzero element in R has a multiplicative inverse. However, in the ideal generated by 'x' in R[x], the constant term (i.e., the term without 'x') is always zero.
This means that the ideal does not contain the multiplicative inverse of any nonzero constant in R. Therefore, the ideal generated by 'x' in R[x] is not equal to R[x], disproving the given statement.
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Related Questions
The hypotenuse of a right triangle is 8 feet long. One leg is 4 feet longer than the other. Find thelength of each leg to the nearest hundredth of a foot.
Answers
Solution:
Given:
\(\text{Hypotenuse}=8\text{feet}\)Let one leg be represented by x.
Hence,
\(\begin{gathered} \text{One leg= x} \\ \text{The other leg is 4 f}eet\text{ longer than the other,} \\ \text{Thus the other leg will be; x + 4} \end{gathered}\)The right triangle can be represented as shown below;
To solve for x, we use the Pythagoras theorem.
\(\text{opposite}^2+adjacent^2=hypotenuse^2\)Hence,
\(\begin{gathered} x^2+(x+4)^2=8^2 \\ x^2+(x+4)(x+4)=64 \\ x^2+x^2+4x+4x+16=64 \\ 2x^2+8x+16=64 \\ \text{Collecting all terms to one side to form a quadratic equation;} \\ 2x^2+8x+16-64=0 \\ 2x^2+8x-48=0_{} \\ \\ \text{Dividing the equation all through by 2,} \\ x^2+4x-24=0 \end{gathered}\)Solving the quadratic equation by formula method,
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)For the equation,
\(\begin{gathered} x^2+4x-24=0 \\ a=1 \\ b=4 \\ c=-24 \end{gathered}\)Substituting these values into the formula,
\(\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-4\pm\sqrt[]{4^2-(4\times1\times-24)}}{2\times1} \\ x=\frac{-4\pm\sqrt[]{16^{}-(-96)}}{2} \\ x=\frac{-4\pm\sqrt[]{16+96^{}}}{2} \\ x=\frac{-4\pm\sqrt[]{112}}{2} \\ x=\frac{-4\pm10.58}{2} \\ x_1=\frac{-4+10.58}{2}=\frac{6.58}{2}=3.29 \\ x_2=\frac{-4-10.58}{2}=\frac{-14.58}{2}=-7.29 \end{gathered}\)Since we are dealing with the length of a triangle, we discard the negative value.
Hence,
\(x=3.29\)The length of one side is 3.29
The other side that is 4 feet longer will be,
\(\begin{gathered} x+4=3.29+4 \\ =7.29 \end{gathered}\)Therefore, the length of each leg to the nearest hundredth of a foot is;
\(\begin{gathered} 3.29\text{ f}eet \\ \\ \text{and} \\ \\ 7.29\text{ fe}et \end{gathered}\)
A number is equal to twice a smaller number plus 3. Yhe same number is equal to twice the sum of smaller number and 1. How many soluyions are possible for this situation
Answers
Answer:
There is no solution to the problem
Step-by-step explanation:
In order to find the solutions to the problem you can write the situation in an algebraic form.
You have that a number is equal to twice a smaller number plus 3. This can be written as follow:
\(x=2y+3\) (1)
where x is the number and y is the smaller number
Furthermore, the same number x is equal to twice the sum of the smaller number and 1, which can be written as follow:
\(x=2(y+1)\) (2)
To find the solution you equal the equation (1) with (2), and you solve for y:
\(2y+3=2y+1\)
\(3=1\)
You obtain an inconsistency, hence, the situation of the problem does not have solution
Hard question: there are many partially mixed strategy Nash equilibria here. Try to think of when players are indifferent between their strategies. In each of the following games, find all the pure and mixed strategy Nash equilibria. Golden Balls Player 2 Split Player 1 Split 50,50 Steal 100,0 Steal 0,100 0,0
Answers
in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).
In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:
If both players choose Split, they both receive a payoff of 50.
If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.
If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.
If both players choose Steal, they both receive a payoff of 0.
To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.
Pure Strategy Nash Equilibria:
(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.
Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.
Mixed Strategy Nash Equilibrium:
To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.
In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.
Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).
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A rectangle has side lengths (x + 7) and (x - 1). The area of the rectangle is 33 square feet. Solve to find the dimensions of the rectangle.
(Be sure to answer all parts.)
a. What equation did you set up to solve this equation?
b. What is the factored form of your equation?
c. What is/are the values of x in this situation?
d. What are the dimensions (side lengths) of the rectangle?
Answers
a. (x+7)(x-1)=33
b. x²+6x-7=33
c. x= -4 or 10
d. 11 by 3
Which is the best estimate for each expression?
24. 37% of 293
Answer choices: B. 120 C. 125 or D. 150
25. 4/5% of 192
Answer choices: A. 2 B. 8 C. 12 or D. 19
Answers
4/5% of 192 is approximately 1.536. The best estimate among the given answer choices is A. 2, which is the closest whole number to the actual value.
To find 37% of 293, we can start by using a proportion. We can set up the proportion as follows:
37/100 = x/293
To solve for x, we can cross-multiply and simplify:
37 x 293 = 100 x
x = 10841/100 ≈ 108.41
So, 37% of 293 is approximately 108.41. The best estimate among the given answer choices is B. 120, which is close to the actual value but slightly overestimated.
To find 4/5% of 192, we can first convert 4/5% to a decimal by dividing by 100:
4/5% = 4/5 ÷ 100 = 0.008
We can then multiply 0.008 by 192 to get the answer:
0.008 x 192 = 1.536
So, 4/5% of 192 is approximately 1.536. The best estimate among the given answer choices is A. 2, which is the closest whole number to the actual value. The other answer choices are too high and would overestimate the value.
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The difference between two numbers is 7. The sum of three times the larger number and twice the smaller number is 16.
Drag and drop the correct options from the list menu to make each statement below true.
Answers
Answer:
28 and 12 . (QUORA)
Step-by-step explanation:
Let’s write this down. We are looking for X and Y.
The difference between two numbers is 16: −=16
Three times the larger number is seven times the smaller: ∗3=∗7
So, we need to solve X and Y from these two equations.
If we re-arrange X*3 = Y*7, we get Y = X*3/7.
So, −∗3/7=16 . −∗3/7 is the same as 7∗/7−3∗/7 , or 4∗/7 . So 4∗/7=16−>4∗=7∗16−>=7∗4=28 .
Then we just go back to −=16 , and =28 , gives us 28−=16, or =28–16−>=12 .
So the numbers are 28 and 12.
two fair dice, each with at least 6 faces are rolled. on each face of each dice is printed a distinct integer from 1 to the number of faces on that die, inclusive. the probability of rolling a sum of 7 is 3 4 of the probability of rolling a sum of 10, and the probability of rolling a sum of 12 is 1 12 . what is the least possible number of faces on the two dice combined?
Answers
Using the Counting the faces of two dice,
the atleast 17 number of faces are possible on the combination of two dice.
First, we have to count the favorable cases,
We know both dice have atleast 6 faces.
It gives 6 favorable cases for a sum of 7.
If we can count them if mean even if dice had more than 6 faces, will matter of for sum of 7.
Now, the mean, we need 6× 4/3=8 (favorable cases for the sum of 10)
If we count 3 favorable cases for each having 6 faces.
For more than 9 faces on a dice matter give the denominator (sample space) are the same for both sum of 7 and the sum of 10, and the probability of one is in proportion to the other.
It mean, additional 5 cases must be ( 7,2), (2,7), (8,2), (2,8) ,(9,1)
So , one of the dice has 8 faces and the other has atleast 9 faces.
Now, we must have atleast 17 combined faces of two dice for probability . So, we get if 12 with configration of 8 faces on one dice.
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A rearview mirror is in the shape of a trapezoid that is 11 inches long across the bottom, 9 inches long across the top, and 3 inches high.
The area of the rearview mirror is
inches squared.fill in the blank
Answers
Answer:
Step-by-step explanation:
“Suppose we covered a large section of wall with chalkboard paint.
How would we find the area we wanted to paint?” Your student might
answer, “Measure how high and how far across, then multiply.” Then
ask, “If one quart of paint covers 65 square feet of wall, how many
quarts would we need to paint the blackboard section with 2 coats?”
Your student would multiply the area by 2 and compare that number
to 65. For example, a blackboard 8 feet wide and 5 feet high is
40 square feet, and 2 coats would be 80 square feet. One can of
paint would not be enough.
• “Suppose we put new carpet in your bedroom. How many square feet
would we need to buy? How would we figure this out?” Your student
might answer, “Measure each wall of the room and multiply. If the
room isn’t a perfect rectangle, divide it into smaller pieces that are
easier to work with.”
Getting your student involved with home projects develops useful skills for
helping around the house, finding a part-time job, and eventually being
responsible for his or her own home.
Enjoy your time working together!
Solve kx + 10 = 7 for x.
Answers
Answer: \(x=\frac{-3}{k}\)
Step-by-step explanation:
To solve for x, you need to get x alone. In this problem, k is a constant.
\(kx=-3\)
\(x=\frac{-3}{k}\)
in a certain region 23 % of people over age 50 didnt graduate from high school . we would like to know if this percentage is the same among the 25-30 year age group use critical value upto 3 decimal places. (a) How many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 8% with 90% confidence? (b) Suppose we wanted to cut the margin of error to 6%. How many people should be sampled now? x (c) What sample size is required for a margin of error of 9% ?
Answers
The goal is to estimate the proportion of non-graduates among the 25-30 year age group. The current known percentage of non-graduates among people over age 50 is 23%.
(a) To estimate the proportion of non-graduates within 8% margin of error and 90% confidence, we need to calculate the required sample size. The formula to determine the sample size for estimating a proportion is:
n = (Z^2 * p * q) / E^2
Where n is the required sample size, Z is the critical value corresponding to the desired confidence level, p is the estimated proportion, q is 1 - p, and E is the desired margin of error.
In this case, Z is the critical value corresponding to 90% confidence level, p is the known proportion of non-graduates among people over age 50 (23%), q is 1 - p, and E is 8%. By plugging in these values, we can calculate the required sample size.
(b) To reduce the margin of error to 6%, we need to recalculate the sample size using the new margin of error. By using the same formula and replacing E with 6%, we can find the updated sample size.
(c) Similarly, to achieve a margin of error of 9%, we can calculate the required sample size by substituting E with 9% in the formula.
By determining the appropriate sample sizes for different margin of error and confidence level combinations, we can ensure that the estimated proportion of non-graduates among the 25-30 year age group is within a desired range with a specified level of confidence.
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HELP PLEASE, if work is needed please add if THANK YOU!!!
Answers
a. If 4 - 5i and -√3 are roots of the polynomial, the other two roots are
4 + 5i and √3b. If polynomial P(x) is divided by x - a, the remainder is zero, then a. x - a is a factor of the polynomial P(x)
What is a polynomial?A polynomial is a mathematical function in which the least power of the variable is 2.
a. Suppose that a polynomial function has four roots and two of its roots are 4 - 5i and -√3. We desire the other two roots. We proceed as follows.
We know that know that complex roots and irrational roots of a polynomial occur in conjugate pairs.
So, since 4 - 5i and -√3 are roots of the polynomial, then their conjugate pairs are also roots.
So, the conjugate pairs are
4 + 5i and √3So, the other two roots are
4 + 5i and √3b. A polynomial P(x) is divided by x - a, the remainder is zero. What can we conclude?
Using the factor theorem, if p(x) is a polynomial and x - a is a linear factor, then if x - a is a factor of p(x), then the remainder when p(x) is divided by x - a is zero.
So, from the above since the remainder when P(x) is divided by x - a is zero, then x - a is a factor of P(x)
So, the answer is a. x - a is a factor of the polynomial P(x)
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\(\frac{4}{\sqrt{13}}\)
Answers
Answer:
\( \frac{4}{ \sqrt{13} } \times \frac{ \sqrt{13} }{ \sqrt{13} } = \frac{4 \sqrt{13} }{13} \)
I hope I helped you^_^
Identify the coefficient, variable, and exponent of the monomial: 4y3
Answers
Answer:
The variable is y since it is a letter and is meant to hold value
The coefficient is 4 since in this equation 4 is multiplied by y
The exponent is 3 since it is after the variable
Hope This Helps!!!
Answer:
The coefficient is 4
The base and variable is y
The exponent is 3
Step-by-step explanation:
4y^3
The coefficient is 4
The base and variable is y
The exponent is 3
A circle with radius of 2 cm sits inside a circle with of 4 cm
Answers
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
how can i solve this
Answers
a. The value of a is 5500. b. The value of r is 0.92. c. There are 2022 trees still alive till 1st October 2023.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
a) The value of a is 5500.
b) To find the value of r, we can use the equation N = ar where N is the number of trees still alive t years after 1st October 2018. We know that N = 5060 on 1 October 2019, so we can substitute these values into the equation:
5060 = 5500 r
r = 5060/5500
r = 0.92
c) To find the predicted percentage decrease in trees still alive between 1 October 2018 and 1 October 2030, we can use the equation:
\(N = ar^t\)
Here a = 5500, r = 0.92 and t = 12
We can now substitute the values, then we get
N = 5500 × (0.92)¹² ≈ 2021.67
N = 2022
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solve for p 3w+4pw=a
Answers
Solve by completing the square:
x^2 + 7x + 4 = 0
Answers
Answer:
x
2
+
7
x
−
4
=
0
Add
4
to both sides of the equation.
x
2
+
7
x
=
4
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
7
2
)
2
Add the term to each side of the equation.
x
2
+
7
x
+
(
7
2
)
2
=
4
+
(
7
2
)
2
Simplify the equation.
Tap for more steps...
x
2
+
7
x
+
49
4
=
65
4
Factor the perfect trinomial square into
(
x
+
7
2
)
2
.
(
x
+
7
2
)
2
=
65
4
Solve the equation for
x
.
Tap for more steps...
x
=
±
√
65
2
−
7
2
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
65
2
−
7
2
Decimal Form:
x
=
0.53112887
−
7.53112887
Step-by-step explanation:
Answer: x= -1 ±√113/14
Eratosthenes was in about 274BC sir Isaac Newton was born in 1642 AD about how many years are they apart ?
Answers
Given: Eratosthenes was in about 274 BC. Sir Isaac Newton was born in 1642 AD.
Required: To determine the difference between both dates.
Explanation: The AD starts right after BC ends. There is no year zero. So we need to count from 247 BC to 1 BC and then 1 AD to 1642 AD.
Thus the difference between the birth dates of Eratosthenes and Sir Isaac Newton is-
\(\begin{gathered} =247+1642 \\ =1889\text{ years} \end{gathered}\)Final Answer: 1889 years.
what is 0.06 divided by 8 working out
Answers
Answer:
0.0075
Step-by-step explanation:
0. 0 0 7 5
_______________________
8 ÷ 0. 0 6 0 0
− 0
_______________________
0 0
− 0
_______________________
0 6
− 0
_______________________
6 0
− 5 6
_______________________
4 0
− 4 0
_______________________
0
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random
sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an
independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If
P, is the proportion of smokers in the population who have had a drink in the past week and P is the
corresponding proportion of non-smokers, then a test of the hypotheses H, P, -P-0 against the two-sided alternative produces a test statistic of z=3.07 and a P-value of 0.002. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and P-value?
a-942, P-value = 0.002
b. -942, P-value-0.004
-3.07, P-value - 0.004
d. -1.75, P-value = 0.002
e-1.75, P-value=0.004
Answers
e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.
A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).
The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).
The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.
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If these two shapes are similar, what is the measure of the missing length d? d 84 cm 10 cm 35 cm
Answers
The missing length in the triangle is 56 cm.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Let us form a proportional equation to find the value of missing length
p/21 = 24/9
Apply cross multiplication
9p=21×24
9p=504
Divide both sides by 9
p=56
Hence, the missing length in the triangle is 56 cm.
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Five employees are available to perform four jobs. The lime it takes each person to perform each job is given in Table 50. Determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs.
TABLE 50
Person
Time (hours)
Job 1
Job 2
Job 3
Job 4
1
22
18
30
18
2
18
—
27
22
3
26
20
28
28
4
16
22
—
14
5
21
—
25
28
Answers
To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.
By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.
Therefore, the optimal assignment would be:
- Person 4 for Job 1 (16 hours)
- Person 2 for Job 2 (18 hours)
- Person 1 for Job 3 (25 hours)
- Person 4 for Job 4 (14 hours)
This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.
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.Line CT and line SM intersect at point A. What is the relationship between angle TAM and angle CAS?
A. Angle TAM and angle CAS are supplementary angles that sum to 180° B. Angle TAM and angle CAS are supplementary angles that are congruent
C. Angle TAM and angle CAS are vertical angles that sum to 180° D. Angle TAM and angle CAS are vertical angles that are congruen
Answers
The relationship between angle TAM and angle CAS is: vertical angles pair, and they are congruent to each other.
Here,
When two straight lines intersect each other at a point, they form four angles. The pair of angles that are directly opposite each other are referred to as vertical angles pair. These angles are congruent to each other. That is, they have the same angle measures.
The image attached below shows the intersection of two lines, line CT and line SM. They intersect at A to form four angles.
Two pairs of vertically opposite angles were formed. angle TAM and angle CAS is one of the vertical angles pair that was formed.
Therefore, the relationship between angle TAM and angle CAS is: vertical angles pair, and they are congruent to each other.
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how do i write a composition of transformations that maps a polygon onto another polygon that are congruent
Answers
Answer:A conductor is mapping a trip and records the distance the train travels over certain time intervals. time (hours) Distance (miles) 0.5 22.5 1 45 1.5 67.545 The train travels at a constant speed. What is its speed in miles per hour?
Step-by-step explanation:
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Solve the problem. 10) Given that P(A or B)= 41 ,P(A)= 81, and P(A and B)= 91 , find P(B). Express the probability as a 10) simplified fraction. A) 7235
B) 72
17
C) 96
7
D) 72
19
Answers
The probability of occurrence of an event B, P(B) for P(A or B)= 1/4,P(A)= 1/8, and P(A and B)= 1/9 is equals the 17/72. So, the correct choice for answer is option(B).
Probability means possibility. It is a branch of mathematics that deals with what happens when an event occurr after a number of trials. It is calculated by dividing the number of favourable outcomes to total number of possible outcomes. It is denoted by P = favourable outcomes/ total number of possible outcomes. If the events A and B are not mutually exclusive, the probability is written as P (A or B) = P(A) + P(B) – P(A and B).
We have, P(A or B)= 1/4 ,P(A)= 1/8 and P(A and B) = 1/9. Using the above probability formula for the union of two events,
=> P (A or B) = P(A) + P(B) – P(A and B).
=> P(B) = P(A or B) - P(A) + P(A and B)
=> P(B) = 1/4 - 1/8 + 1/9
=> P(B) = 13/36 - 1/8
Taking L.C.M for both fraction
=> P(B) = 17/72
Hence, required probability is 17/72.
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are these equations equivalent?
Answers
No, They aren't.
........
There are 36 pencils in a pack that costs $12.82. How much does each pencil cost?
Answers
Answer: each pencil would cost 0.36¢
Step-by-step explanation: first, divide 12.82 by 36 to get the unit rate. The answer should be 0.356111111. Now round that to the nearest cent. 0.356111111~0.36
Answer:
Each pencil is worth 36 cents
Step-by-step explanation:
To do the problem we have to find the unit price which is \(Total Price/Total Units\)
Once you have that round the answer then the answer is 0.36
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What is the constant of proportionality in the table below?
x 5 10 6 9 2
y 15 30 18 27 6
1/3
5
3
15
Answers
Answer:
1/3
Step-by-step explanation:
constant proportionality = x/y
x1/y1 , x2/y2 , x3/y3 , ....
5/15 , 10/30 , 6/18 , 9/27 , 2/6
= 1/3 , 1/3 , 1/3 , 1/3 , 1/3
since in all the cases x/y = 1/3 ,
Therefore, the contant proportionality in the given table is 1/3
Hope it's helpful..
A line has a y-intercept of -2, but has no x-intercept. Describe
this line in words, and sketch its graph.
Answers
Step-by-step explanation:
you will plot -2 on the y axis and x axis is said to be 0.
so our coordinates would be (0,-2).
x^2+3x−10=0 (solve for x)
Answers
Answer:
x1=2 x2=-5
Step-by-step explanation: