The rate of change of the distance between the cars at that instant is 5.46 meters/ second.
The first car's velocity = 7 meters per second
The second car's velocity = 3 meters per second.
Distance from the intersection of first car = 5m
Distance from the intersection of second car = 12m
The rate of change is used to numerically quantify the percentage change in value over a predetermined period of time. It is a measure of a variable's velocity.
Calculating the distance between both cars at the instant
= √(12² + 5²)
= √ 144 + 25
= √169
= 13
Calculating the rate of change of distance -
2d/dt
= d(x² + y²)/dt
= 2x dx/dt + 2ydy/dt
= 2×5×7 + 2×12×3
= 70 + 72
= 142
Therefore, total distance -
dd/dt
= 142/26
= 5.46
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Quadrilateral KLMN has vertices at K(6, 0), L(10, -5), M(5, -9), and N(1, -4).
Is KLMN a square? Justify your answer.
Yes, all sides are congruent, and KL and LM are perpendicular.
Yes, all sides are congruent, and KL and MN are parallel.
No, KL and LM are not perpendicular.
No, KL and MN are not parallel.
We have shown that KLMN has four congruent sides and opposite sides are parallel and perpendicular, which makes KLMN a square.
What is a graph?
A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.
To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.
We can find the length of each side using the distance formula:
KL = sqrt((10 - 6)^2 + (-5 - 0)^2) = sqrt(16 + 25) = sqrt(41)
LM = sqrt((5 - 10)^2 + (-9 - (-5))^2) = sqrt(25 + 16) = sqrt(41)
MN = sqrt((1 - 5)^2 + (-4 - (-9))^2) = sqrt(16 + 25) = sqrt(41)
NK = sqrt((6 - 1)^2 + (0 - (-4))^2) = sqrt(25 + 16) = sqrt(41)
So all four sides have the same length of sqrt(41), which is a necessary condition for a square.
To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:
slope KL = (-5 - 0)/(10 - 6) = -5/4
slope MN = (-4 - (-9))/(1 - 5) = 5/4
slope LM = (-9 - (-5))/(5 - 10) = -4/5
slope NK = (0 - (-4))/(6 - 1) = 4/5
We can see that the slopes of KL and MN are negative reciprocals, as are the slopes of LM and NK. This means that opposite sides are parallel and perpendicular, respectively, which is another necessary condition for a square.
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We have demonstrated that KLMN is a square since it has four congruent sides and opposite sides that are parallel and perpendicular.
What is graph?
A visual representation of the variation of one variable with relation to one or more other variables, such as a collection of dots, lines, line segments, curves, or regions.
To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.
We can find the length of each side using the distance formula:
KL = sqrt((10 - 6)² + (-5 - 0)²) = sqrt(16 + 25) = sqrt(41)
LM = sqrt((5 - 10)² + (-9 - (-5))²) = sqrt(25 + 16) = sqrt(41)
MN = sqrt((1 - 5)² + (-4 - (-9))²) = sqrt(16 + 25) = sqrt(41)
NK = sqrt((6 - 1)² + (0 - (-4))²) = sqrt(25 + 16) = sqrt(41)
So all four sides have the same length of sqrt(41), which is a necessary condition for a square.
To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:
slope KL = (-5 - 0)/(10 - 6) = -5/4
slope MN = (-4 - (-9))/(1 - 5) = 5/4
slope LM = (-9 - (-5))/(5 - 10) = -4/5
slope NK = (0 - (-4))/(6 - 1) = 4/5
We can observe that the slopes of KL, MN, LM, and NK are all negative reciprocals. Another prerequisite for a square is that the opposing sides must be parallel and perpendicular, respectively.
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-11 +23-46+ (-12)
how to solve it
Answer:
-46
Step-by-step explanation:
-11 +23-46+ (-12) =
12 - 46 + (-12) =
-34 - 12 =
-46
Nicolas drinks to third liter of water in the morning and 1/2 liter of water at lunch during basketball practice he drinks another 2/3 liter of water. What is the total amount of water in liters that Nicolas drinks?
Nicolas drinks 3/2 liters of water in total - 1/3 liters of water in the morning, 1/2 liter of water at lunch, and 2/3 liter of water during basketball practice.
Nicolas drinks to third liter of water in the morning, which is 1/3 liters of water. At lunchtime, he drinks 1/2 litre of water. During basketball practice, he drinks another 2/3 liter of water.
To find the total amount of water that Nicolas drinks, we need to add these quantities together:
Total amount of water = 1/3 + 1/2 + 2/3
To add these fractions, we need to find a common denominator, which is 6 in this case. We can convert each fraction to have a denominator of 6 as follows:
1/3 = 2/6
1/2 = 3/6
2/3 = 4/6
Now we can add the fractions with the same denominator:
Total amount of water = 2/6 + 3/6 + 4/6
Total amount of water = 9/6
We can simplify this fraction by dividing both the numerator and denominator by 3:
Total amount of water = 3/2
Therefore, Nicolas drinks 3/2 litres of water in total.
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1- Label the lengths of the 3-on 3 court (perimeter only).
2- Explain how you calculated the court's length and width.
the perimeter of the 3-on-3 court is 86 meters.
Why it is?
The lengths of the 3-on-3 court (perimeter only) are:
Length: 28 meters
Width: 15 meters
To calculate the length and width of the 3-on-3 court, we can use the dimensions provided by FIBA, the international basketball federation. According to FIBA, the official size of a 3-on-3 court is 15 meters in width and 28 meters in length.
The perimeter of the 3-on-3 court is the sum of all four sides, which can be calculated as follows:
Perimeter = 2 × Length + 2 × Width
Substituting the values of length and width from FIBA's dimensions, we get:
Perimeter = 2 × 28 meters + 2 × 15 meters = 56 meters + 30 meters = 86 meters
Therefore, the perimeter of the 3-on-3 court is 86 meters. It's important to note that the dimensions of the court may vary depending on the location and the level of play, so it's always a good idea to check the official regulations before setting up a court.
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18. The signs show the costs of different games at a math festival. How much would it cost n people to play Decimal Decisions and Ratio Rage? MAIHEEST DECITAL PROBABILITY DECISIONS POSSIBILITIES Cost (s) of 1 Game: 12.70 -n +9 Cost(s) of 1 Game: 5.5-3 RATIO RAGE! Cost (5) of 1 Game
The cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 expression Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
The equation "Cost (s) of 1 Game: 12.70 - n +9" gives the cost of playing Decimal Decisions, but we don't know the number of n, thus we can't determine the overall cost for a group of n persons.
Similarly, the cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.
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Find the coordinates of the midpoint of the line segment with the endpoints J(−2, 3) and K(4, −1)
Answer:
jwjwi7svwisg, I have y2ywgeu
For what values of a are the following expressions true(|=absolute value):
Pls help!!!
a. |a-5|=5-a
b.|a|=-a
Answer:
10 is the answer of q u estion
John weighed 156 pounds give or take 8 pounds, ten years ago.
Write the absolute value inequality representing the range of John's weight.
The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.
What is absolute value of inequality?An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.
What is absolute value expression?An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.
As per the given question,
If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.
To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:
| x - 156 | ≤ 8
This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.
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Will give brainlest to first correct answer
Answer: 3
Step-by-step explanation:
3rd, lands on a vowel.
Answer: The spinner lands on a vowel.
Step-by-step explanation:
Probability to land on purple section: 1/10
Probability to land on letter D: 1/10
Probability to land on vowel: 3/10 (A, E, I)
Probability to land on red section: 2/10
3/10 > 2/10 > 1/10
I need to show my work please help
Answer: m= 2 n =7
Step-by-step explanation:
i think to find the answer you can make the sides equal each other so 7m+4 = 9m 2m=4m m =2
and for the other angle
2n-1 = n+6 n - 1 = 6 n = 7
consider a completely randomized design with k treatments. assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. determine the total number of pairwise comparisons for k.
The total number of pairwise comparisons for k is (k*(k-1))/2.
There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.
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Lainey bought a set of
20
2020 markers for
$
6
$6dollar sign, 6. What is the cost of
1
11 marker?
If Lainey bought a set of 20 markers for $6, then the cost of one marker is $0.30.
To determine the cost of 1 marker, we need to divide the total cost of the set of markers by the number of markers in the set.
Lainey bought a set of 20 markers for $6, so the cost of the set is $6. To find the cost of 1 marker, we divide the cost of the set by the number of markers in the set:
Cost of 1 marker = Total cost of set / Number of markers in set
Cost of 1 marker = $6 / 20
Cost of 1 marker = $0.30
Therefore, the cost of 1 marker is $0.30.
In summary, to determine the cost of 1 item in a set, we divide the total cost of the set by the number of items in the set. In this case, Lainey bought a set of 20 markers for $6, so the cost of 1 marker is $0.30.
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Complete question is:
Lainey bought a set of 20 markers for $6. What is the cost of 1 marker?
The organizer of a late night street fair in a popular tourist city wants to analyze the relationship between daily revenue and the following variables: the number of male visitors, the number of female visitors, the number of retail stands, the number of food (and beverage) stands, and the number of performances that take place on a given night. The regression output table is provided below. Based on these results and using a 10% significance level, the organizer thinks he can improve the model. He wants to try removing at least one variable from the analysis to create and compare new models. Which variable or variables would you recommend that he consider removing from the regression model? SELECT ALL THAT APPLY.
The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
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if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 9? (your answer must be in the form of a reduced fraction.)
The probability of selecting a diamond or 9 is 1/13.
Step by step explanation: There are 4 suits (diamonds, clubs, hearts, and spades) and 13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace). The probability of selecting a card from a standard deck of 52 cards is 1/52.
To calculate the probability of selecting a diamond or a 9, you must first calculate the total number of diamonds and nines in the deck, which is 8 (4 diamonds and 4 nines). The probability of selecting a diamond or 9 is 8/52, which reduces to 1/13.
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A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded
annually.
swer:
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answer:
Step-by-step explanation:
(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:
A = P(1 + r)^t
In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:
A = 500(1 + 0.015)^t
Simplifying this gives:
A = 500(1.015)^t
Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.
(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:
500(1.015)^t = 800
Dividing both sides by 500:
(1.015)^t = 1.6
Taking the natural logarithm of both sides:
ln(1.015)^t = ln(1.6)
Using the power rule of logarithms:
t ln(1.015) = ln(1.6)
Dividing both sides by ln(1.015):
t = ln(1.6) / ln(1.015)
Using a calculator:
t ≈ 24.7
Therefore, it takes approximately 24.7 years for the account balance to reach $800.
Find the Value of N
134 + 427 = N
12 x N = 60
12 + N + 48 = 100
180 ÷ 2 = N
75 ÷ N = 15
N ÷ 10 = 50
( 4 x 100 ) + N = 600
120 - N = 20
10 + N - 3 = 12
N - ( 4 x 5 ) = 30
Step-by-step explanation:
1)561
2)5
3)40
4)90
5)3
6)500
7)200
8)100
9)5
10)50
Parallelogram RKMT has an area of 343 units^2 . RKMT is dialated by a scale factor of 2/7 . What is the area of the resulting image
Therefore , the solution of the given problem of area comes out to be the area of the resulting picture is therefore 28 units.
What is an area exactly?By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.
Here,
The following algorithm determines the area of a parallelogram:
=> Base area * height
We can write: given that the trapezoid RKMT has an area of 343 units2,
=> Base(RKMT) x Height(RKMT) = Area(RKMT) = 343
All of the parallelogram's linear measurements (lengths and widths) are multiplied by 2/7 when it is dilated by a scale factor of 2/7. As a result, the expanded parallelogram's base and height will be as follows:
=> base(dilated) equals base x (2/7)(RKMT)
=> Height(dilated) = Height * (2/7)(RKMT)
The dilated parallelogram's size will be as follows:
=> Area(dilated) = base(dilated) x height(dilated)
=> (2/7) x base(RKMT) x (2/7) x height(RKMT)
=> (4/49) x Area(RKMT)
=> (4/49) x 343
=> 28
The area of the resulting picture is therefore 28 units2.
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The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires (Tire Rack website, February 3, 2009). The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again. (Data is in TireRack file)
1. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship. Interpret the coefficients (Say what they mean in terms of change in you corresponding to a change in x)
2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
4. Is the addition of the Tread Wear independent variable significant? Use 0.05 level of significance.
1 Tire Steering read WeaBuy Again 2 Goodyear 8.9 8.5 8.1 3 Michelin F89 9 8.3 4 Michelin H 8.3 8.8 8.2 5 Dunlop SI 8.2 8.5 7.9 6 Goodyear 7.9 7.7 7.1 7 Yokoham 84 8.2 8.9 8 Yokoham 7.9 7 7.1 9 Kumho P 7.9 7.9 8.3 10 Goodyear 7.6 5.8 4.5 11 Hankook 7.8 6.8 6.2 12 Michelin E 7.4 4.8 13 IMichelin N7 14 Michelin S 6.9 15 Kumho 776.6 16 Dunlop SI 6.2 4.2 17 Bridgestof 5.7 5.5 18 Goodyear 5.7 5.4 19 Dunlop SI57 5 5 34 3.6 2.9 3.3
Tire Steering Tread Wear Buy Again
Goodyear Assurance TripleTred 8.9 8.5 8.1
Michelin HydroEdge8.9 9 8.3
Michelin Harmony 8.3 8.8 8.2
Dunlop SP 60 8.2 8.5 7.9
Goodyear Assurance ComforTred 7.9 7.7 7.1
Yokohama Y372 8.4 8.2 8.9
Yokohama Aegis LS4 7.9 7 7.1
Kumho Power Star 758 7.9 7.9 8.3
Goodyear Assurance 7.6 5.8 4.5
Hankook H406 7.8 6.8 6.2
Michelin Energy LX4 7.4 5.7 4.8
Michelin MX4 7 6.5 5.3
Michelin Symmetry 6.9 5.7 4.2
Kumho 722 7.2 6.6 5
Dunlop SP 40 A/S 6.2 4.2 3.4
Bridgestone Insignia SE200 5.7 5.5 3.6
Goodyear Integrity 5.7 5.4 2.9
Dunlop SP20 FE 5.7 5 3.3
Show transcribed image text
The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.
The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.
The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.
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A five feet tall woman is walking towards a 20 feet tall street lamp at a rate of 3ft/s. The distance between her and the street lamp is labeled by x and the length of her shadow which the lamp casts is labeled by y. Answer the following questions about this situation.Which of the following equations represents a relationship between dy/dt and dx/dt ?A. dy/dt = 1/3 *dx/dt B. dy/dt = 3 *dx/dt C. dy/dt = 4*dx/dt D. dy/dt = 1/4 *dx/dt
The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).
Woman is walking towards the street lamp.
Rate at which the length of her shadow is changing as she walks.
Let us consider the height of the street lamp as h = 20 feet.
Height of the woman be w = 5 feet.
And the distance between the woman and the street lamp be x.
Length of the woman's shadow be y.
Triangles formed by the woman, the street lamp, and their shadows are similar.
Sides of similar triangles are in proportion,
This implies,
h / y = (h + w) / (x + y)
Solving for y we get,
⇒h(x + y) = y(h + w)
⇒hx + hy = hy + wy
⇒y = hx / w
Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,
⇒ dy/dt = h(dx/dt) / w
Substitute in the values for dx/dt = 3 ft/s, h and w we get,
⇒dy/dt = (20)(3) / 5
⇒dy/dt = 60 /5
⇒dy/dt =12
⇒dy/dt = 4(3)
⇒dy/dt =4× (dx/dt)
Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .
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Fay read an article that said 26%, percent of Americans can speak more than one language. She wants to test if this figure is higher in the city she lives, so she plans on taking a sample of people to see what proportion of them speak more than one language.
Let p represent the proportion of people in Fay's city that speak more than one language.
Which of the following is an appropriate set of hypotheses for her significance test?
Answer:
The appropriate set of hypotheses for Fay's significance test is:
Null Hypothesis: p = 0.26 (the proportion of people in Fay's city who can speak more than one language is the same as the national average)
Alternative Hypothesis: p > 0.26 (the proportion of people in Fay's city who can speak more than one language is higher than the national average)
In other words, Fay is testing if the proportion of people in her city who speak more than one language is significantly different from the national average of 26%. The null hypothesis assumes that the proportion is the same as the national average, while the alternative hypothesis assumes that it is higher.
To conduct her significance test, Fay would need to collect a random sample of people from her city and determine how many of them speak more than one language. Based on this sample proportion, she can calculate a test statistic and determine if it is significantly different from what would be expected under the null hypothesis. If the test statistic is sufficiently large, she can reject the null hypothesis and conclude that the proportion of people in her city who speak more than one language is higher than the national average.
Step-by-step explanation:
Answer:4
Step-by-step explanation:
4
can someone help pls 16=3x-7/2
Answer: To solve the equation 16=3x-7/2, you can follow these steps:
Multiply both sides of the equation by 2 to get rid of the fraction:
16 * 2 = (3x - 7/2) * 2
32 = 6x - 7
Add 7 to both sides of the equation to isolate the term with x:
32 + 7 = 6x
39 = 6x
Divide both sides of the equation by 6 to solve for x:
39 / 6 = x
6.5 = x
Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]
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[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]
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━━━━━━━━━━━
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[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]
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• Substituting the value of (x) in the given equation,
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[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]
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As LHS = RHS,
Hence Verified
The grades on a midterm were Normally distributed with a mean of 120 and a standard deviation of 17. The passing score was 111 or higher. Use the z-table to answer the question.
What percent of students passed the midterm?a. 10%
b. 50%
c. 70%
d. 62%
The percentage of students passing the partial exam is:
Option c. 70%
What is the percentage of students passing the partial exam?To answer this question, we use the Z-table. We have:
Given, mean (μ) = 120 and standard deviation (σ) = 17
Passing Score = 111
To find out what percentage of students passed the midterm, we need to find the probability that a score picked at random from the distribution is greater than or equal to 111. We can convert this score into a standard score (Z-score) using the Z-table. We have:
Z-score = (111 - μ) / σ
= (111 - 120) / 17
= -0.53
Using the Z-table, we can find the area (probability) to the left of this Z-score as follows:
Area to the left of Z-score = 0.2981 (from Z-table)
The area to the right of this Z-score (i.e. the probability that a score picked at random from the distribution is greater than or equal to 111) is:
Area to the right of Z-score = 1 - 0.2981
= 0.7019
= 70.19%
Therefore, the percentage of students who passed the midterm is approximately 70% (Option C).
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Answer:
C. 70%
Step-by-step explanation:
consider the following page reference string: 0, 1, 7, 0, 1, 2, 0, 1, 2, 3, 2, 7, 1, 0, 3, 1, 0, 3 how many page faults would occur for the following page replacement algorithms? assume no pre-paging occurs, and show what pages are in memory at each given time. three frames are allocated to the process.
a. fifo b. optimal c. lru
Will rate after, make sure answer is correct show work
In the following question, among the conditions given, For the page reference string provided, the number of page faults for the following page replacement algorithms are as follows: A. FIFO: 8-page faults, B. Optimal: 6-page faults, C. LRU: 7-page faults.
To learn about them in brief-
A. FIFO: 8-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 0, 1, 2
Step 7: 0, 1, 2
Step 8: 0, 1, 3
Step 9: 2, 7, 1
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
B. Optimal: 6-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 2, 3
Step 6: 1, 2, 3
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 1, 0, 3
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
C. LRU: 7-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 1, 0, 2
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 2, 0, 3
Step 10: 2, 1, 0
Step 11: 2, 1, 3
Step 12: 0, 1, 3
Step 13: 0, 2, 3
Step 14: 1, 2, 3
Step 15: 1, 0, 3
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What is the value of X?
Answer: 8
Step-by-step explanation:
The sum of the interior angles in a triangle in 180.
So we can add up all the values and set it equal to 180 to find x.
4x + (5x + 5) + 103 = 180
9x + 108 = 180
9x = 72
x = 8
Answer:
x=8
Step-by-step explanation:
4x+5x+5+103=180
9x+108=180
9x=180-108
9x=72
x=72÷9
x=8
n one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?a.Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 daysb, Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 dayc. Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 dayd. Approximately normal with mean 5.5 days and standard deviation 2.6 dayse. Approximately normal with mean 5.5 days and standard deviation 0.26 day
(e): Approximately normal with mean 5.5 days and standard deviation 0.26 days.
What is standard deviation?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean or average. It measures how far the values in a dataset are from the mean of the dataset.
The sample size needed for this approximation to hold depends on the shape of the population distribution, but a commonly used rule of thumb is that a sample size of at least 30 is sufficient for most cases.
In this case, the sample size is 100, which is larger than 30, so we can use the central limit theorem to approximate the sampling distribution of the sample mean.
The mean of the population distribution is 5.5 days, and the standard deviation is 2.6 days. The standard deviation of the sampling distribution of the sample mean can be approximated using the formula:
standard deviation of the sample mean = standard deviation of the population / square root of sample size
= 2.6 / sqrt(100)
= 0.26
Therefore, the best description of the sampling distribution of x is option (e): approximately normal with mean 5.5 days and standard deviation 0.26 days.
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PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
A graph of Triangle ABC after a dilation with a scale factor of 1/2 and center of dilation at D (-5, 5) is shown in the image attached below.
What is dilation?In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the point D (-5, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate A, we have;
Coordinate A = (1, -1) → (1/2(1 - (-5)) + (-5), 1/2(-1 - 5) +5)
Coordinate A = (1, -1) → (1/2(6) - 5, 1/2(-6) + 5)
Coordinate A' = (-2, 2).
For coordinate B, we have;
Coordinate B = (1, -3) → (1/2(1 - (-5)) + (-5), 1/3(-3 - 5) +5)
Coordinate B = (1, -3) → (1/2(6) - 5, 1/2(-8) + 5)
Coordinate B' = (-2, 1).
For coordinate C, we have;
Coordinate C = (3, -3) → (1/2(3 - (-5)) + (-5), 1/3(-3 - 5) +5)
Coordinate C = (3, -3) → (1/2(8) - 5, 1/2(-8) + 5)
Coordinate C' = (-1, 1).
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Solution of inequality ((x - 1)(x - 5))/(x - 3) > 0
Answer:
(1, 3) ∪ (5, ∞)
Step-by-step explanation:
You want the solution to the inequality ((x -1)(x -5))/(x -3) > 0.
Sign changesThe sign of the function changes at values of x that make the factors zero, at x = 1, 3, 5. The function is positive for x > 5, so will also be positive for 1 < x < 3
The solution is ...
1 < x < 3 or 5 < x
__
Additional comment
If any linear factor has an even degree (even multiplicity), there will not be a sign change. The numerator factors correspond to function zeros. The denominator factors correspond to function vertical asymptotes.
The attached graph shows zeros at x=1 and x=5, and a vertical asymptote with a sign change at x=3.
A 64-foot tall monument casts a shadow 16 feet long. If Kyle is standing nearby and 6’3” tall, find the length of his shadow.
All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T
What is the monument casts a shadow?The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.
Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.
We can use proportions to solve the problem.
Let x be the length of Kyle's shadow.
We know that the length of the monument's shadow is 16 feet, and its height is [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:
[tex]16/64 = 1/4[/tex]
This ratio is equal to the ratio of Kyle's shadow length to his height:
[tex]x/6.25 = 1/4[/tex]
To solve for x, we can cross-multiply:
[tex]x = 6.25/4 = 1.5625[/tex]
Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or [tex]18.72 inches)[/tex] .
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how can i slove this??
Answer:
[tex]5x {}^{3} - x + 5x + 2[/tex]
Step-by-step explanation:
Greetings!!!
So to find the sum of (f+g)(x) just simply add these two functions
f(x)+g(x)3x²+5x-2+(5x³-4x²+4)Add like terms together
5x³-x²+5x+2If you have any questions tag it on comments
Hope it helps!!!
Could you please answer b and d
I will mark brainliest for the first answer
Answer: 50 uk pounds
Step-by-step explanation:
Step-by-step explanation:
See image below