Answer: 3 negative residuals and 5 positive residuals
Step-by-step explanation: When the observed number is lower than the predicted number then this is an example of a negative residual. The tricky thing is this doesn't make much sense you would think that this would be a positive residual but it's not to that's something you need to remember!
example
observed number: 10
predicted number: 10.5
this is a negative residual and it's the opposite for the positive residual
The data set has 2 negative residuals and 6 positive residuals. which is the correct answer would be an option (A).
What are the residuals?A residual is a difference between the observed value and the predicted value for a given data point. The sign of the residual indicates whether the predicted value is above or below the observed value.
The table defines the observed data values and the corresponding predicted values, based on a regression line of fit.
Observed Predicted
9 7.77
12 12.87
12 11.17
15 14.57
17 16.27
24 24.77
28 26.47
33 31.57
In this case, the residuals for the data points would be calculated as follows:
Observed value - Predicted value = Residual
9 - 7.77 = 1.23 (positive)
12 - 12.87 = -0.87 (negative)
12 - 11.17 = 0.83 (positive)
15 - 14.57 = 0.43 (positive)
17 - 16.27 = 0.73 (positive)
24 - 24.77 = -0.77 (negative)
28 - 26.47 = 1.53 (positive)
33 - 31.57 = 1.43 (positive)
Based on these calculations, there are 2 negative residuals (-0.87 and -0.77) and 6 positive residuals (1.23, 0.83, 0.43, 0.73, 1.53, and 1.43).
Therefore, the data set have 2 negative residuals and 6 positive residuals.
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suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. a study was then done to see if the mean time has increased in the new century. a random sample of 27 first-time convicted burglars in a recent year was picked
We can reject the null hypothesis at the 0.05 level and accept the alternative hypothesis.
A one-sided test will test using the full alpha to test whether the result is far enough in one direction. A two-sided test will split the alpha in half to test whether the result is too big or too small.
The null hypothesis is:
[tex]\mathit{H}_{0}: \mu= 2.5[/tex]
The alternative hypothesis is:
[tex]\mathit{H}_{1}: \mu > 2.5[/tex]
The z-score for a mean of 3 is:
[tex]z = (x- \mu)/ (\sigma/ \sqrt{n})) \\ = (3-2.5)/(1.8/\sqrt{n})) \\ = (.5)/(1.8/6)) \\ = (.5)/(.3)) \\ = 1.666666667[/tex]
The z-score for the 0.05 significance level is 1.645, which is less than the mean of 3 z score of 1.67.
Hence, we can go ahead and reject the null hypothesis
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A triangle on a coordinate plane is translated according to the rule tâ€"3, 5(x, y). which is another way to write this rule? (x, y) → (x â€" 3, y 5) (x, y) → (x â€" 3, y â€" 5) (x, y) → (x 3, y â€" 5) (x, y) → (x 3, y 5)
The translation rule, T₋₃,₅ (x,y) for a given triangle on the coordinate plane can be written as
(x, y) → (x – 3, y + 5)
that is x-coordinate shifts to left on x-axis and y-coordinate shifts upward on y-axis. So, the correct option is option ( A).
Translation:
Figure translation is horizontal, vertical, or both movement of the graph or figure. Figures can be moved left, right, up, or down.
Steps to Perform a Translation on the Coordinate Plane are :
Identify the vertices of the shape in the diagram.Apply horizontal translation to the x-coordinate of each vertex in the figure. If you shift the number left, you need to subtract the amount of left shift from the x coordinate. If you shift the number right, you have to add the correct amount of shift to the x coordinate.Apply vertical translation, if you are transforming a number up, you need to add the amount you are transforming to the y coordinate. If you're transforming a number down, you'll need to subtract the amount you're transforming from the y coordinate. Select the graph with correctly transformed vertices from the options given.We have given that
A triangle say ABC is translated on coordinate plane according to following rule, T₋₃,₅ (x, y)
Another way to wright this is explained below. As we know that translation is represented
Tₕ,ₖ(x,y) = (x+h, y+k) which implies that x coordinate shifts to left h point and new coordinate is x+h.
Similarly, new y corrdinate will be y+k
Now, for our point ,
T₋₃,₅ (x,y) ---shifted---> ( x-3 , y+5)
=> (x, y) → (x – 3, y + 5)
Hence , the coordinates of new trangle say A'B'C' which is translation of triangle ABC with coordinates (x,y) are ( x-3 , y+5).
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The Equation P=5s represents the perimeter P of a regular pentagon with side length S. what is the perimeter of a regular pentagon with side length 3 centimeters (CM)
*constant of proportionality*
The Perimeter of the Pentagon is 15 cm
What is a Pentagon?A pentagon is a geometrical shape, which has five sides and five angles
The equation P=5s represents the perimeter P of a regular pentagon with side length s.
We are to find the perimeter of a regular pentagon with side length of 3 cm.
To find it, put s = 3 cm in the given equation.
P = 5(3) cm
P = 15 cm
Hence, the perimeter of the regular pentagon of side length 3 cm is 15 cm.
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The perimeter of a regular pentagon with side length of 3 cm is 15 cm.
How to find the perimeter of a pentagon?A pentagon is a polygon with 5 sides. A regular pentagon is a pentagon with all sides and angles equal to each other.
The Equation P = 5s represents the perimeter P of a regular pentagon with side length s.
The perimeter of a regular pentagon with side length of 3 centimetres can be calculated as follows:
P = 5s
where
P = perimeter of a pentagons = side length of the regular pentagonTherefore,
P = 5(3)
Perimeter of the regular pentagon = 15 cm.
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complete the following statements. in general, % of the values in a data set lie at or below the 62th percentile. % of the values in a data set lie at or above the 76th percentile.. if a sample consists of 900 test scores, of them would be at or below the 56th percentile. if a sample consists of 900 test scores, of them would be at or above the 40th percentile.
In general, 62% of the values in a data set lie at or below the 62th percentile. 76% of the values in a data set lie at or above the 76th percentile. If a sample consists of 900 test scores, 504 of them would be at or below the 56th percentile. If a sample consists of 900 test scores, 540 of them would be at or above the 40th percentile.
What is percentile?A percentile is a comparison score among a particular score and the scores of the rest of a group. It presents the percentage of scores which a particular score surpassed. For example, if you score 85 points on a test, and are ranked in the 75th percentile, this means that the score 85 is higher than 75% of the scores. In general, percentile defines the percentage of a data set which is below or at a value which is being considered.
Thus, the percentage of the values of a data set that lies below or at the 62th percentile is 62%.
And also, the values of a data set that lies below or at the 76th percentile is 76%.
Given a sample of 900 test scores, the number of test scores that will be at or below the 56th percentile is 56% of 900 which is mathematically represented as:
n = 56% x 900
n = 56/100 x 900
n = 504 test scores
Given a sample of 900 test scores, the number of test scores that will be above the 40th percentile is (100 - 40 = 60) % of 900 which is mathematically represented as:
n = 60% x 900
n = 60/100 x 900
n = 540 test scores
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when reading a table for bivariate analysis that displays percentages of some attributes, what is the rule of thumb for reading the table?
Bivariate table is that which shows the relationship between two variables. The rule of thumb... if the table is scaled down by percentage, read the whole thing. If the table is percentages, read it down.
Bivariate table:
A table that depicts the relationship between two variables by showing the distribution of one variable over the categories of a second variable.
Bivariate Table Primary Purpose:
A bivariate table shows the distribution of one variable over the categories of another variable.
Finally, we mentioned that univariate data can be displayed in many different ways, such as bar charts and box plots. Bivariate data, on the other hand, are usually displayed in scatter plot.
Rule of thumb:
Bivariate analysis results can be represented in form of a two-column data table.
A rule of thumb when reading spreadsheets created by others is then spreadsheet is percentage down, read the whole thing. If the table is percentages, read it down.
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What is the term for the price at which the quantity demanded for a product is equal to the quantity supplied?.
The only price at which consumer and producer plans can be reconciled is the equilibrium price, which is reached when the quantity of the good that consumers wish to purchase, or quantity demanded, equals the quantity that producers wish to sell, or quantity supplied. The equilibrium quantity is the name given to this common quantity..
What is equilibrium quantity?
When a product is in equilibrium quantity on the market, there is neither a shortage nor an excess. When supply and demand coincide, the quantity of a good that customers desire to buy and the quantity that its suppliers are supplying are the same.What are the equilibrium quantity and price?
The only price at which consumer and producer plans coincide is the equilibrium price, which is reached when the quantity of a good that consumers want to buy (quantity demanded) . the quantity of a good that producers want to sell (quantity supplied) are equal. The equilibrium quantity is the name given to this common quantity.Learn more about equilibrium quantity
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a swimming pool is circular with a 30-ft diameter. the depth is constant along east-west lines and increases linearly from 4 ft at the south end to 9 ft at the north end. find the volume of water in the pool. (round your answer to the nearest whole number.)
This circular swimming pool has 4595 ft³ of water in it.
Define the term circular volume?The formula V=r² can be used to determine a cylinder's volume (h). Determining the area of both the circular bottom shape then multiplying it by the height is all that's required to calculate a cylinder's volume.According to what is said, the depth grows linearly from 2 feet at the south end to 7 feet at the north end and remains constant along east-west lines.
The given data in the question-
Diameter of circular swimming Pool; d = 30 ft
Radius r = d/2 = 30/2 = 15 ft
The average depth is given as;
avg (h) = (4 + 9)/2
avg (h) = 6.5 ft
Formula for circular area is;
A = πr²
Put the values;
A = π × 15²
A = 225π
Formula for circular volume is;
Volume = Area × depth
Volume = 225π × 6.5
Volume = 4594.57 ft³
Rounding to a whole number;
Volume = 4595 ft³
Thus, this circular swimming pool has 4595 ft³ of water in it.
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1 million tons sample of coal contains 1% sulfur. if you have 1 million tons of coal how much of gas is so2 produced
3750 tons of SO₂ are produced for one million tons of coal burned.
All living things, including humans, are composed of carbon. However, as coal burns, its carbon reacts with airborne oxygen to generate carbon dioxide. Although carbon dioxide (CO2) is an odorless, colorless gas, it is one of numerous gases in the atmosphere that can retain the heat from the planet.Coal is most frequently and significantly used in combustion, where heat is produced to create steam, which in turn powers the turbines that generate electricity.For the purpose of heating or cooking, burning coal within the house releases particle and gas emissions that may contain a variety of hazardous substances, including benzene, carbon monoxide, formaldehyde, and polycyclic aromatic hydrocarbons.To know more about coal burn
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you are to use the erdpml: a diver exits the water at 1:30 p.m. after a dive to 63 feet for 35 minutes. he reenters the water at 2:20 p.m. for a dive to 55 feet for 25 minutes. how soon could the diver reenter the water for a dive to 50 feet for 38 minutes?
After 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.
What is eRDPML?
The Electronic Recreational Dive Planner Multi Level, or simply eRDPml, is a novel programme created by PADI to help you correctly plan your dives. FOR MANY. An electronic version of the PADI dive tables may be more convenient for certain divers than having to recall how to use them.
If a diver exits the water at 1:30 pm after a 35-minute dive to 19 metres utilising the eRDPML, he will be in pressure group P.
At 2:20 PM, he returns to the ocean. His surface interval is 50 minutes, according to this. A diver in pressure group P switches to pressure group G after 50 minutes.
He will then be in pressure group S if he stays at 17 metres for another 25 minutes. Go to the Surface Interval Mode to find out how long must be spent above the surface before the third dive.
After the second dive, join the pressure group S and start the third dive at a depth of -15 metres for 38 minutes.
33 minutes are determined to be the necessary surface interval. A 33 minute surface interval after the second dive places the diver in pressure group K before the third dive, completing the dive profile.
Hence, after 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.
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FILL IN THE BLANK. to test if there is a difference in two population means, a ___should be used. anova one sample t test two sample t test none of the above
To test if there is a difference in two population means, a difference in sample mean should be used , the correct option is (b) .
In the question ,
we have to find the what is used to test whether their is a difference in two population means or not .
For each hypothesis problem, there is test statistic .
This test statistic is compared to the critical value to make the decision about the hypothesis.
Hence choosing the appropriate test statistics matters a lot.
Here two samples are there. It is clearly given for which we have to test the hypothesis that is sample means .
Hence, we can say that the test statistic is, the difference in sample mean .
Therefore , the difference in sample mean is used to test if there is a difference in two population means .
The given question is incomplete , the complete question is
To test if there is a difference in two population means, a ___ should be used.
(a) alpha
(b) the difference in sample means
(c) the degrees of freedom
(d) the difference in the population means
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Felicia and Geraldine ran 32 miles this week. Geraldine ran 17 miles.
Which equation should you use to find out how many miles Felicia ran?
A). x-32=17
B). x+32=17
C). x-17=32
D). x+17=32
Answer:
D). x+17=32
Step-by-step explanation:
32 is the total
and Geraldine and Felicia together would get 32
so, Felicia ran D). x+17=32 in an equation
What is a practical in research?.
The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry is referred to as practical research.
In the given question we have to define practical in research.
The development of information applicable to activity that upholds by the fundamental elements of scientific inquiry—clearly specified research questions, reliable patterns of thought, methodical data collecting and analysis, and acceptable conclusions—is referred to as practical research.
Practical research aims to advance knowledge through scientific theories, concepts, and ideas in order to benefit society. Establishing hypotheses, gathering data, evaluating, etc. all serve practical research purposes.
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ten observations were selected from each of three populations, and an analysis of variance was performed on the data. the following are part of the results. source of variation sum of squares degrees of freedom mean square f between treatments 82.4 within treatments (error) 158.4 total
The MS error in the variance is 5.867 using ANOVA
What is Analysis of Variances(ANOVA )?
ANOVA is a statistical method for determining if the effects of different independent variables on a given dependent variable differ or correlate. ANOVA can be used in finance in a variety of ways, such as to forecast price changes in securities by first identifying the variables that affect stock variations. This study can be a useful tool for understanding how a securities or market index will behave in certain scenarios.
Treatment = k-1=2 The degree of freedom
N-k=30-3=27 for the error degrees of freedom
N-1 = 29 degrees of freedom in total.
MS Therapy = (SS Therapy /df Therapy)
82.4/2 = 41.2
MS error = (SS error/df error)
158.4/27 = 5.867
Hence the MS error in the variance is 5.867
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Create all of the possible arrays for modeling a rectangular quilt with the 24 paper squares. write an equation to accompany each array. you can use the attached pre-made quilt squares by cutting and pasting them, or you can draw the arrays with your own designs on a separate sheet of paper.
The array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.
The array can be taken as rows.
If we take the first side as the length denoted by L and the second side as the width indicated by W.
Then the area can be given as;
Area = length * width
Area = L * W
The total area of the quilt is 24 squares which can be obtained as;
24 × 1 = 24
All squares are arranged in a single row.
(r³ - 3) × 1 = 24
12 × 2 = 24
12 squares arranged in 2 rows.
(r² + 3) × 2 = 24
8 × 3 = 24
8 squares arranged in 3 rows.
(r² - 1 ) × 3 = 24
6 × 4 = 24
6 squares arranged in 4 rows.
(r² - 3 ) × 4 = 24
3 × 8 = 24
3 squares arranged in 8 rows.
(r) × 8 = 24
2 × 12 = 24
2 squares arranged in 12 rows.
(r - 1 ) × 12 = 24
1 × 24 = 24
1 square arranged in 24 rows.
(r - 2) × 12 = 24
In all of the above r = 3.
Thus, the array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.
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the results of a recent poll on the preference of shoppers regarding two products are shown below. product shoppers surveyed shoppers favoring this product a 800 560 b 900 549 find the point estimate for the difference between the two population proportions in favor of this product.
The point estimator for the difference between two populations proportion in favor of this product is 0.09.
In the given question, the results of a recent poll on the preference of shoppers regarding two products are shown below.
Product Shoppers Surveyed Shoppers Favoring this Product a 800 560
b 900 549
We have to find the point estimate for the difference between the two population proportions in favor of this product.
n(1)=800, x(1)=560
n(2)=900, x(2)=549
P(1)=x(1)/n(1)
P(1)=0.7
P(2)=x(2)/n(2)
P(2)=0.61
The point estimator for the difference between two populations proportion in favor of this product is
P(1) - P(2)=0.7-0.61
P(1) - P(2)=0.09
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Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0.98; Ha: p > 0.98; α = 0.05). The test results in a p-value of 0.15. However, the company is unaware that it is actually producing 99% high-quality candy. What MOST likely happens as a result of the testing? A. The company rejects H0, making a Type I error. B. The company fails to reject H0, making a Type II error. C. The company rejects H0, making a Type II error. D. The company fails to reject H0, making a Type I error. E. The company rejects H0 correctly.
The company fails to reject H0, making a Type II error. So the option B is correct.
In the given question,
Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0.98; Ha: p > 0.98; α = 0.05).
The test results in a p-value of 0.15.
However, the company is unaware that it is actually producing 99% high-quality candy.
We have to find MOST likely happens as a result of the testing.
The given options are:
A. The company rejects H0, making a Type I error.
B. The company fails to reject H0, making a Type II error.
C. The company rejects H0, making a Type II error.
D. The company fails to reject H0, making a Type I error.
E. The company rejects H0 correctly.
The company will not be rejecting the null hypothesis when it should have been, given the P-value is approaching 0.05.
Hence, the business commits a Type II error by failing to reject H0.
So the option B is correct.
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a closed cylindrical can is to hold 1000 cubic cm. of liquid. what should be the height and radius of the can to minimize the total surface area.
The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm
The volume of the cylinder can = 1000 cubic cm
Consider the height of the cylinder as h and the radius of the base is r
Volume of the cylinder = π[tex]r^2[/tex]h = 1000
h = 1000 / π[tex]r^2[/tex]
The surface area of the cylinder
A = 2π[tex]r^2[/tex] + 2πrh
A = 2π[tex]r^2[/tex] + 2πr(1000 / π[tex]r^2[/tex] )
A = 2π ( [tex]r^2[/tex] + 1000 / π[tex]r^2[/tex])
Differentiate the terms
A' = 2π (2r + 1000 / π[tex]r^3[/tex])
When the minimum surface area
2π (2r + 1000 / π[tex]r^3[/tex]) = 0
r = [tex](1000/2\pi )^\frac{1}{3}[/tex]
r = 5.41 cm
Then,
h = 1000 / π[tex]r^2[/tex]
= 1000 / (π × 5.41 × 5.41)
= 1000 / 91.94
= 10.87 cm
Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm
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What type of congruent postulate in which two corresponding angles and non-Included side of the two triangles are congruent?.
The congruent postulate in which two corresponding angles and non-Included side of the two triangles are congruent is AAS. AAS is an abbreviation of angle angle side postulate.
Triangles are said to be congruent if they are of identical sides and angles. The three sides of first triangle are exactly equal in measure to the three sides of second triangle. The three angles of first are each the same angle as the second triangle.
Triangles are said to be congruent when all corresponding sides and interior angles are congruent. The triangles will have same shape and size, but the first triangle may be a mirror image of the other triangle.
The definition of Angle Angle Side Theorem also states that-
If two angles and the non-included side of first triangle are congruent to the corresponding parts of second triangle, then the triangles are said to be congruent.
Other theorems which triangles follow are Side Angle Side, Side Side Angle, Angle Side Side, Side Side Side, Angle Angle Angle etc.
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a. leon goes to the clothing store to buy a new t-shirt, for which he is willing to pay up to $10. he picks out one he likes with a price tag of exactly $10. when he is paying for it, he learns that the t-shirt has been discounted by 50%.
The consumer surplus is $5.
Consumer surplus is defined as the amount saved based on the estimated value and actual paid price. It is the difference between the amount that customer wants to pay and the amount that customer has to pay based on the final price.
Leon is willing to pay $10. The discount offered of $10 item is 50%. Hence, the final price will be -
Final price = 10 - 50%×10
Final price = 10 - 5
Final price = 5
Surplus amount = 10 - 5
Surplus amount = $5
Thus, the surplus amount for Leon is $5.
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The complete question is -
Determine the amount of consumer surplus generated: Leon goes to the clothing store to buy a new T-shirt, for which he is willing to pay up to $10. He picks out one he likes with a price tag of exactly $10. When he is paying for it he learns that the T-shirt has been discounted by 50%
which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?
The answer to the given question is nominal and ordinal measurements. These two type measurements are used to group respondents or objects into groups or categories and also considered as categorical measures.
What is nominal measurement?Nominal measurement is the least accurate and informative, because it only names the characteristic or identity which we are interested. In nominal variables, the numerical values just "name" the attribute differently. Thus, numerical value is simply a label.
What is ordinal measurement?Ordinal measurement reports the ranking and ordering of the data without chartering the degree of variation. Ordinal measurement includes statistical data type in which variables are in order or rank but without a degree of difference between categories. The ordinal measurement includes qualitative data. This measurement places variables in order or rank, and only allowing to measure the value as higher or lower in measurement.
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Mariam is going to invest $3,000 and leave it in an account for 13 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Mariam to end up with $6,200?
The interest rate that would be earned each month on the amount invested is 0.47%.
What is the interest rate?When the money invested in an account earns a compound interest, it means that both the amount invested and the interest that has already being earned increases 12 times in a year. When an investment earns at a compound interest, it grows exponentially.
The formula that can be used to determine the interest rate is :
Interest rate = [(future value / amount invested)^(1/n)] - 1
Where n is the number of periods
Number of periods = number of years x compounding period
Number of periods = 13 x 12 = 156
Number of periods = [(6200 / 3000)^(1/156) ] - 1 = 0.47%
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How do you solve an inequality step by step?.
The steps for solving inequality is consisting of four steps which are elaborated below :
The first step of solving an inequality is to Eliminate divisions by multiplying all terms by the slightest common denominator of all fractions, then the next step is to Simplify by combining like terms on each side of the inequality, then subtract or add quantities to get the unknown on one side and the numbers on the other, the next step is to divide each term of the inequality by the coefficient of the unknown, just In case the coefficient is positive, the inequality will stay the same or if the coefficient is negative, the inequality will be reversed.
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Kevin had 55 ¼ boxe of admiion form in inventory a month ago. Now he ha 27 5/8 boxe left. How many boxe have been ued?
Boxes used in one month is 221/8 as fraction.
What is mixed fraction?
A fraction portrayed with its quotient and remainder may be a mixed fraction. as an example, two 1/3 may be a mixed fraction, wherever two is that the quotient, one is that the remainder. So, a mixed fraction may be a combination of a full range and a correct fraction.
Main body:
Initial boxes with kevin = 55 1/4
converting mixed fraction in simple fraction = 55[tex]\frac{1}{4}[/tex]
= 221/4
Total boxes left = 27[tex]\frac{5}{8}[/tex]
converting it ,
=27 [tex]\frac{5}{8}[/tex] = (27*8+5)/8
=221/8
Total boxes used = 221/4 - 221/8
taking L.C.M , we get
=442-221/8
= 221/8
Hence total boxes used = 221/8
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What two numbers add up to 72?.
Answer:
-1 + 73 =72
-2 + 74 = 72
-3 + 75 = 72
Ayden is preparing for a job interview later today. He is deciding what to wear to the interview. He has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes. If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, how many different outfits can ayden make?.
Answer:
144
Step-by-step explanation:
This is the counting principle.
Multiply the numbers of the items together.
6 × 4 × 3 × 2 = 144
Which inequality is true?.
Inequality is use when we are not sure about the exact date of a given sample.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
For example:
If the cost of a Jersy = $40
Cost of Hat = $15
The softball team has a total of $1,200 to spend.
Let x equal the number of jerseys the team orders and y equal the number of hats the team orders.
So the total money will be spent within the budget will be
40*x + 15*y ≤ $1200
Hence, the inequality model will be 40*x + 15*y ≤ $1200.
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What is the solution to the system of equations y 1. 5x 4 y =- X?.
The solution of the given equations y=1.5x-4 and y=-4 is given by the coordinates (x,y) as (0, -4)
Illustrate System Of Equations.
A system of equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.
[tex]y=1.5x-4 , y=-4[/tex]
Substitute the value of y as - 4
-4=1.5x-4
Solving for x, by transposing the terms we get
1.5x = - 4 + 4
1.5x = 0
x = 0
Therefore, the solution is (0, -4).
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40 x 7 = _________ x 10 x 7
40 x 7 = _________ x 10 x 7
280 = ? x 70
280 = 4 x 70
check: 280 = 280
4 goes in the blank
Answer:
4
Step-by-step explanation:
40×7=280
10×7=70
280:70=4
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
Total subscribers that Netflix must sample to obtain the interval to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows are 385 subscribers.
For the Wald-type confidence interval, the confidence limits are:
[tex]p-[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex] , [tex]p+[/tex][tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Where p is the sample proportion attended, n is the sample size, and z∗α/2 is the upper α/2 quantile of the standard normal distribution for a 100 (1−α) % confidence interval. If a 95% CI is needed, this corresponds to α = 0.05, thus
[tex]z_{\alpha /2}[/tex] ≈ 1.96
And, the quantity
ME = [tex]z_{\alpha /2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
is studied as the margin of error. Since we also need ME ≤ 0.05, we solve for n to acquire
n ≥ p (1 − p) [tex](\frac{z \alpha /2}{ME} )^{2}[/tex]
The only undetermined quantity is p; but since p (1 − p) ≤ 1/4 for all p ∈ [0,1], we identify that a sample size of at least
n ≥ [tex](\frac{z \alpha /2}{2ME} )^{2}[/tex]
undertakes the Wald interval will have a margin of error less than the needed margin no matter the sample proportion checked. Alternating the given values results in
n ≥ [tex](\frac{1.96}{2(0.05} )^{2}[/tex] = 384.16
for that we need to round up to guarantee the sample size is enough, thus n = 385.
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What is the solution to the system of equations y 3x 25x 2y 15?.
The solution to the given system of equations y=-3x-2 and 5x+2y=15 is given by the coordinates as [tex](-19,55)[/tex]
What is a System Of Equations ?
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Define Subsitution Method .
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Define Elimination Method.
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
The solution to the system of equations y = -3x - 2 and 5x + 2y = 15
Given:
[tex]y=-3x-2[/tex] - (1)
[tex]5x+2y=15[/tex] - (2)
Here we are using substitution method to proceed with the given problem ,
So,
⇒[tex]5x+2(-3x-2)=15[/tex]
⇒[tex]5x-6x-4=15[/tex]
By further calculation
⇒[tex]-x=15+4[/tex]
⇒[tex]x=-19[/tex]
Substituting x value in (1)
⇒[tex]y=(-3)(-19)-2[/tex]
By further calculation
⇒[tex]y=57-2[/tex]
⇒[tex]y=55[/tex]
Therefore, the solution is [tex](-19,55)[/tex].
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