The solutions are x = ±1.73, ±3.87.
Given equation: x4 − 10x2 + 9 = 0
Rewrite equation as (x2 - 9)(x2 + 1) = 0
Set each factor equal to 0 and solve for x
x2 - 9 = 0
⇒ x2 = 9
⇒ x = ±3.87
x2 + 1 = 0
⇒ x2 = -1 ⇒
x = ±1.73
The given equation is x4 − 10x2 + 9 = 0. This can be rewritten as (x2 - 9)(x2 + 1) = 0. By setting each factor equal to 0 and solving for x, we get x2 - 9 = 0 which implies x2 = 9 and x = ±3.87. Similarly, x2 + 1 = 0 implies x2 = -1 and x = ±1.73. Therefore, the solutions of x4 − 10x2 + 9 = 0 are x = ±1.73, ±3.87.
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76 pencils come in a box. If 4 teachers share 3 boxes equally, how many pencils does each teacher
receive?
Answer:
The total number of pencils is 76 x 3 = 228 pencils
If each teacher receives an equal amount of pencils, we can divide the total number of pencils by the number of teachers to find how many pencils each teacher receives:
228 pencils / 4 teachers = 57 pencils/teacher
Each teacher receives 57 pencils.
The Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Based upon the input from Units 1 and 2, you have just received your next assignment that will contribute to your next decision. For the outdoor sporting goods client, based upon your prior decision on whether or not to expand to the next market or retain your current position, justify your decision further utilizing the chi-square distribution tool. One key criterion point: You do not have adequate data to formulate a full chi-square for the outdoor sporting goods client. However, you have sufficient data to initiate this process. You are charged to demonstrate the initial steps of a nonparametric test that are qualitative. Utilizing the null and alternative hypotheses, further present your justifications for your selection and what it means beyond the mere formulas. What is this going to tell the Board of Directors and contribute to the decision-making process? The following information may be helpful in understanding chi-square and hypothesis testing: Please review this helpful video. The presenter uses flipping a coin and rolling a die. These are examples and analogies used in the CTU resources. The following are assumptions that might make the assignment more helpful and make the responses more uniform: Continue to utilize the Big D scenario. Work under the assumption that the sample is based upon 2 different proposed product lines. Additionally, work under the assumption that the same demographics are utilized for each product.
My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.
Because we put our alternative hypothesis equal to what we wish to show, you should continue to hold the stance you already hold. The opposite hypothesis, or null hypothesis, is a claim that there is no difference. For instance,There is no discernible difference between the mean and sample population, according to the null hypothesis.Alternative Hypothesis H1: The mean and sample population differ significantly.Level of significance: A: If there is no difference in the sample as well as population means, there is a 5% chance that the null hypothesis will be rejected. In a non-parametric test, rankings are considered as a test statistic after being translated from the observed sample. We utilize the rankings to calculate the test statistic in non-parametric testing. The choice of accepting or the null hypothesis being rejected will be decided when the levels of liberty and crucial values have been defined. Chi square is used since there are only two choices to compare. As soon as we get our data, we can calculate the chi squared value x2 and determine the crucial values from table of freedom levels with 95% certainty.To know more about hypothesis visit:
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your favorite restaurant has a promotion where you can win free food. you will roll 2 dice. the sum of the 2 dice will determine which prize you receive. 2-column table with 11 rows. column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. column 2, probability, entries startfraction 1 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 6 over 36 endfraction, startfraction 5 over 36 endfraction, startfraction 4 over 36 endfraction, startfraction 3 over 36 endfraction, startfraction 2 over 36 endfraction, startfraction 1 over 36 endfraction. which scenario uses the addition rule for mutually exclusive events? p(rolling a sum of 4) p(rolling a sum of 4 or rolling a sum of 5) p(rolling a sum of 12 or rolling a double 6) p(rolling a sum of 11 and rolling a sum of 12)
Answer: P(rolling a sum of 4 or rolling a sum of 5)
Step-by-step explanation: edge2023
The scenario that uses the addition rule for mutually exclusive events is:
p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)
This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.
The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36
The other scenarios do not use the addition rule for mutually exclusive events:
p(rolling a sum of 4) is a single event and does not involve a second event.
p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.
p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.
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Determine the probability of tossing two heads in a row by:
Listing all possible outcomes ((H,T), (H,H) and so on) and circling the desired outcome.
Calculating desired outcome
--—----------------
Total number of outcomes
Answer:
4
Step-by-step explanation:
(H,H) (T,T)(T,H)(H,T)
A student is assessing the correlation between the average number of hours of internet browsing and the average score on a math test. The table below shows the data:
Number of hours of internet browsing
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Score on math test
(y) 95 94 93 92 91 90 89 88 87 86
Part A: Is there any correlation between the average number of hours of internet browsing and the average score on the math test? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)
1. There is a correlation that exists between the average number of hours of internet browsing and the average score on the math test.
2. The function that best fits the data is: Y = f(X)
3. The slope and the intercept tells us that a student would be at their best in a test if they spent 0 hours browsing.
How to find the correlation in the data set1. The correlation that exists in this data set tells us that as a person spends more time on the computer, they would spend less time on their test preparation. This would eventually affect their score.
When the student did not browse the internet, they had their highest score in math. As they started to spend more time on the internet, the score started to drop.
2. The function is given as
math test score Y = function of X: hours spent browsing the internet
this is written mathematically as:
Y = f(X)
3. The Y intercept is at the point where the student spent 0 hours browsing. this is the point where they did their best in this test. This tells us that if a student spent 0 hours on the internet, they would do their best in the test.
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State the domain of A. (Assume the length of the rectangle is longer than its width. Enter your answer in interval notation) 14. 0/2 points Previous Answers CalcETS 1.1.058. Find a formula for the described function. A rectangle has area 36 m2 Express the perimeter of the rectangle as a function of the length L of one of its sides PIL) = || State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.) Submit Answer 15. 0/2 points Previous Answers CalcET8 1.1.061. Find a formula for the described function. An open rectangular box with volume 3 m has a square base Express the surface area SA of the box as a function of the length of SA 26 Xma State the domain of SA. (Enter your answer in interval notation.)
Previous question
The answer is CalcETS 1.1.058.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel. Since, a rectangle is a 2-D shape, it is characterized by two dimensions, length, and width. Length is the longer side of the rectangle and width is the shorter side.In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
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The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared with customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let pEspresso= the true proportion of customers who drink espresso and use their own cup and pCoffeee = the true proportion of customers who drink coffee and use their own cup. The P-value for this significance test is 0.033. Which of the following is the correct conclusion for this test of the hypotheses
The owner should reject the null hypothesis since 15 < 24. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should fail to reject the null hypothesis since 15 < 24. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
The owner should fail to reject the null hypothesis since 0.033 < 0.05. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup
Correct option is: b
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
This can e solved using the concept of null-hypothesis.
What is null-hypothesis?Using a single observable variable to compare two sets of observed data and measurable phenomena, the null hypothesis is a common statistical theory that contends that no statistical link and significance exists.
A hypothesis that a link of some sort exists between the variables is where scientists start their inquiry. The alternative, known as the null hypothesis, claims that there isn't any such link. Despite its uninteresting appearance, null hypothesis is a crucial component of research.
The correct hypotheses to test the owner's claim is as follows:
H0: pExpress - pCoffee = 0
Ha: pExpress - pCoffee < 0
Since p-value = 0.0330 < 0.05, we reject the null hypothesis.
Thus, the correct option for this hypothesis test is:
The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.
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Since 0.033 < 0.05, the owner should reject the null hypothesis. The genuine percentage of customers who drink espresso and bring their own cups is clearly lower than the true percentage of customers who drink coffee and bring their own cups.
What is the null hypothesis?The null hypothesis is a widely used statistical theory that asserts that no statistical relationship and significance exists when two sets of observed data and measurably occurring occurrences are compared.
Scientists begin their investigation with the presumption that there is some form of relationship between the factors. The alternative, often known as the null hypothesis, contends that such a connection doesn't exist. The null hypothesis, although appearing dull, is an essential part of the research.
The following are the proper assumptions to test the owner's assertion:
H0: pExpress - pCoffee = 0
Ha: pExpress - pCoffee < 0
Since p-value = 0.0330 < 0.05, we reject the null hypothesis.
Thus, the correct option for this hypothesis test is:
Since 0.033 < 0.05, the owner should reject the null hypothesis. There is strong proof that the actual percentage of consumers who order an espresso and bring their own cups is far lower than the actual percentage of customers who order coffee and bring their own cups.
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find an equation of the tangent line to the given curve at the specified point. y = e^x /x , at the point (1, e)
An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.
Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.
To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:
y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2
Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:
y' = (e - e/1) / 1^2
y' = e
Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.
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Solve each triangle using the Law of Cosines.
two arithmetic sequences and both begin with and have common differences of absolute value , with sequence increasing and sequence decreasing. what is the absolute value of the difference between the st term of sequence and the st term of sequence ?
The difference between the 51st term of a and the 51st term of b is 1000.
the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]
where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference
Given that,
[tex]a_{0}=b_{0}=30[/tex]
Common difference of both series that have absolute value = 10
common difference of series a is 10 as this series is increasing
similarly, the common difference of series b is -10 as it is decreasing
Putting the values in the above equation we get:
[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*10
=> 30 + 500 = 530
Thus, the value of [tex]a_{51}[/tex] is 530.
[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]
=> 30 + (51-1)*-10
=> 30 -500 = -470
Thus, the value of [tex]b_{51}[/tex] is -470.
so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000
Therefore, The difference between the 51st term of a and the 51st term of b is 1000.
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What do I put in the boxes?
jake sold 28 tickets to the school fair, and jeanne sold 21 tickets. what is the ratio,in simplest form
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3
The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.
To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.
So, the simplified ratio is 28/7: 21/7 = 4:3
So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.
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1. The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.
The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. The 99% confidence interval is (0.3162, 0.5238). There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%. The 99% confidence interval is (0.3162, 0.5238). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238). The 99% confidence interval is (0.4762, 0.6838). We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%. The 99% confidence interval is (0.4762, 0.6838). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838).
The first statement is correct. The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. However, the rest of the statements are incorrect.
"There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%." is incorrect, this statement is about a probability of a single student, but the confidence interval is about a probability of the whole population.
"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238)." is correct, this statement is true, but it doesn't add any additional information.
"The 99% confidence interval is (0.4762, 0.6838)." is incorrect, this value is not the correct confidence interval.
"We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%." is incorrect, this statement is not true, as the confidence interval is not (0.4762, 0.6838) but (0.3162, 0.5238)
"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)." is incorrect, as this is not the correct confidence interval.
In conclusion, the faculty members at McAdenville High School can be 99% confident that the true proportion of students who will attend the Winter Formal is between 31.62% and 52.38%.
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Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
10 jars
Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.
Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
⚠️Please verify inthe comments if there was indeed a 4th option⚠️
Answer:
8
Step-by-step explanation:
convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.
Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.
Is 1 a factor of all number?
1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself.
Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.
Every number other than 1 has at least two factors, namely the number itself and 1.
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The sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚. Work out the size of each of the eight interior angles.
The eight interior angle based on the information given will be 728°.
How to calculate the angle?From the information, the sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚ and.we.wany to eork out the size of each of the eight interior angles
In this case, it should be noted the octagon has with sides. This will be Illustrated as:
= (n - 2) × 180
= (8 - 2) × 180
= 1080
The eight interior angle will be:
= 1080 - (42 + 110 + 13 + 67 + 55 + 11 + 54)
= 1080 - 352
= 728
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Find the solutions of the given equation.
25x² +64 = 289
O A. x =
-√√3, √3
OB.
x =
-9,9
OC.
x = -3, 3
O D. x = -3√3, 3√/3
The solution of the given equation is x = -3,3. Hence option C is the correct option.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.
The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.
Given equation is
25x² +64 = 289
Subtract 64 from both sides of the equation:
25x² +64 -64 = 289 -64
25x² = 225
Divide both sides by 25:
25x²/25 = 225/25
x² = 9
Take square root on both sides:
√x² = √9
x = ±3.
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the probability of randomly picking out a paperback book from a bookshelf is 2 over 5. what are the odds in favor of choosing a paperback book? a.) 3:2 b.) 2:7 c.) 2:3 d.) 2:5
Therefore , selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
What does the process of probability mean?Calculating the probability of an event happening or a declaration being true is the focus of the mathematical field of probability theory. A chance is just a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating the likelihood of an event occurring. Probability is a mathematical expression of the likelihood or probability that because an event will take place. The percentage ranges of 0% to 100% as well as the numerals 0 and 1 can be used to describe probabilities. the percentage of times an event occurs in a perfect collection of equally likely alternatives, out of all possible outcomes.
Here,
Given The likelihood of selecting a paperback book at random from either a bookshelf is 2/5, as stated.
In order to determine whether picking a paperback book is more likely to be strange,
So, using the information provided, we observe it.
that the odd favor of picking a paperback book is 2:1.
Option D is the proper choice.
Since selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.
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Answer:
2:3
Step-by-step explanation:
Four friends drove from their homes in four different cities to a class reunion.Who drove the fastest?MarenSafiyaTomasCam
Tomas drove the fastest with the speed of 70 miles per hour.
What is speed?
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
The formula for calculating speed is -
Speed = Distance / Time
Maren travels 60 miles in 1 hour.
Speed of Maren = 60/1
Speed of Maren = 60 miles per hour
Safiya travels 120 miles in 3 hour.
Speed of Safiya = 120/3
Speed of Safiya = 40 miles per hour
Tomas travels 84 miles in 1.2 hour.
Speed of Tomas = 84/1.2
Speed of Tomas = 70 miles per hour
Cam travels 75 miles in 1.5 hour.
Speed of Cam = 75/1.5
Speed of Cam = 50 miles per hour
Therefore, the fastest driver is Tomas.
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A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.
How to calculate the quantity of units using quadratic equations?The net income of the company in thousands of dollars is represented with the function;
f(x) = 9x2 – 54x – 144,
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, hence:
x + 2 = 0 -> x = -2.
x - 8 = 0 -> x = 8.
The positive value and not a negative shows that there are amount of products sold which should be = 8.
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For every pound a company spends on advertising, it spends £0.24 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answer:
25:6
Step-by-step explanation:
1/0.24
100/24
50/12
25/6
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 7 0-9 3 10 9 ; 2=lambda = 7, 10 0 0 10
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
what is matrix ?Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array. In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.
given
Eigen values ( λ )
| A - λI | = 0
= ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0
= λ = 7 , 11 , 11
eigen vector for λ = 7
( A - IB ) X = 0
= Let y = 1 , n1 = ( -1 1 0 )
eigen vector for λ = 11
( A - λI ) X = 0
n2 = ( 0 1 0 ) let n3= ( -2 0 1 )
D = ( 7 0 0 , 0 11 0 , 0 0 11 )
The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).
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A coin-operated coffee vending machine dipene, on the average, 6 oz of coffee per cup. Can thi tatement be true of a vending machine that occaion
It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.
The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.
It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.
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What are types of solutions?
There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.
Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.
Types of solutions:
No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.
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26 over 100 in simplest form
Circle O shown below has a radius of 30 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 1.8 radians.
30 inches
0=1.8 rad
Answer:
To the nearest tenth of an inch, the length of the arc is 54.0 inches
Step-by-step explanation:
To determine the length of the arc, x, we need to use the formula for arc length, which is:
arc length = radius * angle (in radians)
Therefore,
arc length = 30 inches * 1.8 radians = 54 inches
Last summer, there were 888 houses for sale in Neil's town. The other 37 houses in the town were not for sale. What percentage of the houses in Neil's town were for sale last summer?
Answer:
96% of the houses were up for sale.
Step-by-step explanation:
Total number of houses
888 = 37 = 925
888 / 925 = .96
You change a decimal into a percent by multiplying by 100%
.96 x 100% = 96%
A man is 38 years old, and his daughter is 14 years old. How many years will it be before the man's age is just twice the age of his daughter?
This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.
Algebraic word problemIn algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.
We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;
38 + x = 2(14 + x) {open bracket}
38 + x = 28 + 2x
38 - 28 = 2x - x {collect like terms}
10 = x
also x = 10.
Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.
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the length of a rectangle is 4 inches shorter than its width. the perimeter of the rectangle is 80 inches. what are the length and width of the rectangle?
If length of a rectangle is 4 inches shorter than its width and perimeter of rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .
The Perimeter of rectangle can be calculated by using formula : [tex]2(l+w)[/tex] ;
let the width of rectangle be = w ,
it is given that the length is 4 inches shorter than width , that means ;
the width of rectangle is ⇒ [tex]w-4[/tex] ;
So , the perimeter becomes ⇒ [tex]80=2(l+w)[/tex]
⇒ [tex]80=2(w-4+w)[/tex]
⇒ [tex]40=2w-4[/tex] ;
⇒ [tex]2w=44[/tex] ;
⇒ [tex]w=22[/tex] ;
and substituting [tex]w=22[/tex] , we get [tex]l=22-4 = 18[/tex] in
Therefore , the length of rectangle is 18 in and width is 22 in .
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