Answer:
$210 when round up
Step-by-step explanation:
To find the total estimate for the repairs, we need to add up the cost of each individual repair.
Wheel alignment: $110
Transmission fluid flush: $75
Cabin air filter: $23
Total estimate = $110 + $75 + $23 = $208
Pam rounded the costs to the nearest $10, so the total estimate may not be exactly $208, but it will be close to it.
Directions: Solve for x. Round to the nearest tenth.
Answer:
x = 73
Step-by-step explanation:
Since it's asking for the angle it's going to be inverse (sin-1,cos-1,tan-1)
It only gives you the opposite side and the hypotenuse
You can find the opposite side by going opposite from the missing angle like basically the side that is not being touched by x (The 4) This is the opposite angle
The hypotenuse is always going to be the long angle that is on the opposite side of the right angle (The 6) This is the hypotenuse
The adjacent side is the side not opposite to the x
Remember the acronym SOH CAH TOA
sin-opposite/hypotenuse
cos-adjacent/hypotenuse
tan-opposite/adjacent
The opposite and hypotenuse are the only sides that gave a number so it is sin and is inverse
[tex]sin^{-1} (\frac{4}{6} ) = .729[/tex]
hope this helps
SOLVE BY INDIRECT PROOF 1. If n – m is even, then n^2 – m^2 is also an even.2. If x is odd positive integer then x^2 – 1 is divisible by 4. 3. If x is an odd integer, then 8 is a factor of x^2 – 1. 4. Suppose x, y E Z. If x is even, then xy is even.
All statements can be proven by indirect proof. If the assumptions of the statement are false, the resulting contradiction proves that the initial assumption is wrong and the statement is true.
1. To prove this statement by indirect proof, assume that n – m is an even number but n^2 – m^2 is an odd number. Since n – m is even, it can be written as n – m = 2k, where k is an integer. This can be substituted into n^2 – m^2 = n^2 – (2k+m)^2 to create n^2 – m^2 = n^2 – 4km – m^2. Since both n and m are integers, 4km is an even number. This means that n^2 – m^2 is an even number, contradicting our assumption that it is an odd number. Therefore, our initial assumption is wrong, and n^2 – m^2 must be an even number if n – m is even.
2. To prove this statement by indirect proof, assume that x is an odd positive integer but x^2 – 1 is not divisible by 4. Since x is an odd positive integer, it can be written as x = 2k + 1, where k is an integer. This can be substituted into x^2 – 1 = (2k + 1)^2 – 1 to create x^2 – 1 = 4k^2 + 4k. Since both k and 4 are integers, 4k^2 is an even number. This means that x^2 – 1 is divisible by 4, contradicting our assumption that it is not divisible by 4. Therefore, our initial assumption is wrong, and x^2 – 1 must be divisible by 4 if x is an odd positive integer.
3. To prove this statement by indirect proof, assume that x is an odd integer but 8 is not a factor of x^2 – 1. Since x is an odd integer, it can be written as x = 2k + 1, where k is an integer. This can be substituted into x^2 – 1 = (2k + 1)^2 – 1 to create x^2 – 1 = 4k^2 + 4k. Since 8 is a factor of 4k^2, it is also a factor of x^2 – 1. This means that 8 is a factor of x^2 – 1, contradicting our assumption that it is not a factor of x^2 – 1. Therefore, our initial assumption is wrong, and 8 must be a factor of x^2 – 1 if x is an odd integer.
4. To prove this statement by indirect proof, assume that x is an even integer but xy is an odd number. Since x is an even integer, it can be written as x = 2k, where k is an integer. This can be substituted into xy = (2k)y to create xy = 2ky. Since both k and y are integers, 2ky is an even number. This means that xy is an even number, contradicting our assumption that it is an odd number. Therefore, our initial assumption is wrong, and xy must be an even number if x is an even integer.
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what is the slope through the line of (-8, -11) and (-1, -5)
The slope of the line through the points (-8, -11) and (-1, -5) is (y2 - y1)/(x2 - x1) = (-5 - (-11))/(-1 - (-8)) = -6/7 = -0.8571428571428571.
Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table. 1 2 8 Characteristic Cluster 2 3 7 Magnesium Flavanoids Proanthocyanins Colorintensity
Cluster 1 has average magnesium, flavanoids, and proanthocyanins levels, while Cluster 2 has low levels of these compounds, and Cluster 3 has high levels of these compounds. Colorintensity levels vary across clusters.
Cluster 1 has an average level of magnesium, flavanoids, and proanthocyanins. This means that the levels of these compounds are not particularly high or low. Cluster 2 has a lower level of these compounds than Cluster 1, so wines in this cluster would have a milder taste than Cluster 1. Cluster 3 has a higher level of these compounds than Cluster 1, resulting in a more intense flavor. The colorintensity of wines in each cluster can also vary, with darker or lighter wines depending on the cluster. Gatsby’s categorization system is based on these average characteristics, allowing him to determine the flavor and color of wines in each cluster.
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The perimeter of the shape is 51.42 cm
Calculate the value of the diameter d.
Take to be 3.142
TU
Answer:
The perimeter of a circle is equal 2 * pi * radius. So, if we let "d" be the diameter of the circle, we can use the following to solve for the radius:
Perimeter = 2 *p * radius = 51.42 cm
we can then use the relationship between the diameter and the radius to solve for the diameter:
d = 2 * radius
substitute the value of the perimeter equation into the diameter equation:
d= 2 * (51.42 cm / 2 * 3.142)
d= 33.49 cm
therefore, the diameter d is 33.49 cm
Find an expression which represents the difference when (2x + 4) is subtracted
from (4x + 2) in simplest terms.
Answer:
(-2x+2) is the difference
Step-by-step explanation:
Shown above
given a list of clothing items [a, b, c, ...] and a list of illegal outfits [[a, b], [a, c], ...], return the number of legal outfit combinations. a combination has to have at least 1 outfit and must not contain any illegal combination.
The objective of backtracking, an algorithmic methodology, is to find every possible solution to a problem by applying the "brute force" method.
What is backtracking used for?
Crosswords, verbal arithmetic, Sudoku, and many other puzzles that need constraint fulfilment may all be solved using backtracking. For parsing, the knapsack problem, and other combinatorial optimization issues, it is frequently the most practical method.
The objective of backtracking, an algorithmic methodology, is to find every possible solution to a problem by applying the "brute force" method. It entails gradually compiling a collection of each answer. A issue would have limits, so any solutions that don't meet them would be eliminated
.
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A man cover 255 km in 6 hours on scooter at a uniform speed find his speed in kilometres per hour
Answer:
The man's speed is 42.5 km/h.
You can find this by dividing the distance he traveled (255 km) by the time it took him to travel that distance (6 hours).
255 km / 6 hours = 42.5 km/h.
The formula to find speed is:
Speed = Distance / Time
In this case, the distance is 255 km and the time is 6 hours. So using the formula, we can calculate the speed as:
Speed = 255 km / 6 hours = 42.5 km/h
So the man's speed is 42.5 km/h.
12feet 4ft what’s the pitch
The area of the football pitch can be found to be 48 ft ²
How to find the area ?The area of the scaled model of the football pitch can be found by using the formula for the area of a rectangle . This is because the scaled model of the pitch takes the form of a rectangle .
The area would therefore be :
= Length x Width
Length = 12 ft
Width = 4 ft
Area of the football pitch model is ;
= 12 x 4
= 48 ft ²
In conclusion, the area of the pitch is 48 ft ² .
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The full question is:
A scaled model of a football pitch measures 12 feet 4 ft. What's the pitch area?
The wind chill Index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v)
Estimating : Ft( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30⁰c
when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises
estimating: Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15⁰c
when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by 0.15⁰c for every km/h that the wind speed
A) Estimating the values of Ft(−15, 40) and fv(−15, 40)
To estimate the value of Ft( -15,40 ) we have to take an average value hence Ft ( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30
and this means that when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c that the actual temperature rises
To estimate the value of Fv(-15,40 ) we have to take an average value
hence Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15
and this means that when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by about 0.15⁰c for every km/h that the wind speed.
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The complete question is :
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). (a) Estimate the values of fT(−15, 40) and fv(−15, 40). (Round your answers to two decimal places.) fT(−15, 40) ≈ fv(−15, 40) ≈ What are the practical interpretations of these values? When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature ---Select--- by about °C for every degree that the actual temperature rises. When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature.
ana lopez borrow $5000 for 75 days at 8% exact interest find how much interest she must pay on the loan and how much will be die at maturity?
To find the interest Ana must pay on the loan, we can use the formula:
Interest = Principal x Interest Rate x Time (in days) / 365
What's the math rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.
In this case:
Interest = $5000 x 8% x 75 / 365 = $200
So, Ana must pay $200 in interest on the loan.
To find the total amount due at maturity, we add the interest to the principal:
Total Due = Principal + Interest = $5000 + $200 = $5200
So, Ana will need to pay $5200 at maturity.
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Can someone help? I’m stuck on these. I’ll give brainliest!!
The system of equations is y = - x - 5 and y = - x - 9.
y = - 4/3 x - 1/3 and y = - 5/4x + 1/4.
what is meant by equations?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.a formula that expresses the connection between two expressions on each side of a sign.Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.Any equation's general form includes the degree of variables in descending order. A linear equation has the general form an x + b = 0.To learn more about equations refer to
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: find the point on a directed line segment between two given points that partitions the segment in a given ratio.
The point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
Given two points P1(x1,y1) and P2(x2,y2), the point that partitions the directed line between these two points in a given ratio r can be calculated using the following formula:
P(x,y) = (x1 + r(x2-x1), y1 + r(y2-y1))
For example, if we have P1(1,2) and P2(4,6) and we want to partition the line in a ratio of 1:3, the point P(x,y) can be calculated as follows:
P(x,y) = (1 + 1/3(4-1), 2 + 1/3(6-2)) = (1.333,3.333)
Therefore, the point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
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Solve and graph. --6x < 21
[tex]-6x < 21[/tex]
Divide both sides by -6:
[tex]\dfrac{-6x}{-6} < \dfrac{21}{-6}[/tex]
[tex]x > -\dfrac{7}{2}[/tex], [tex]x > -3.5[/tex]
Heather , deon and trey sent a total of 109 text messages over their cell phones during the weekend. Trey sent 3 times as many messages as deon. Deon sent 9 fewer messages than heather . How many messages did they each send
Answer:
Deon sent 20 messages
Trey sent 60 messages
Heather sent 29 messages
Step-by-step explanation:
Explanation above
Customer 1 and customer 2 each buy products X and Z.
Product Y is never sold to customers who buy product Z.
Conclusion:
Product Y is never sold to customers 1 and 2.
If the assumptions are true, is the conclusion
A) Correct
B) Cannot be determined based on the information available
C) Incorrect
If the assumptions are true, the conclusion is correct.
What assumptions are true?A statement that is included in an argument as an assumption is one whose truth value is (temporarily) accepted as True. The word "let" is frequently used in mathematics to indicate the introduction of an assumption. Let p, for instance (be true). An extreme circumstance is assumed to solve a problem using the Assumption Method (also known as the Supposition Method) in Singapore Math. Comparing this strategy to the Guess and Check method that primary school pupils learn in Primary 3, it is frequently thought of as a quicker substitute.We are informed that
Each of customers 1 and 2 purchases products X and Z.
Customers who purchase product Z are never offered product Y.
The resulting conclusion is that Customers 1 and 2 are never sold Product Y.
According to the information provided, Customer 1 purchased Products X and Z.
Client 2 purchased Products X and Z.
Customers of product Z are unable to purchase product Y.
Therefore, it is obvious that neither customer can buy product Y when they both purchased Z.
Therefore, the conclusion is correct if the presumptions are true.
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Find the volume of a square based pyramid with a base length of 7 and a height of 12
Answer:
V=a2h3
Step-by-step explanation:
For a nonnegative real number x > 0, let {x} denote its fractional part. For instance, {1.2345} = 0.2345, {n} = 0.14159..., {} = 0.4, and so on.
The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.
What is an exponential parent function?
The simplest parent function of an exponential function takes the form:
f(x)= p ^x , where p refers to the base.
So, if we have a number such that x = 3 and the base is 2
f(3) = 2³
f(3) = 6
Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).
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help me solve this pls
Answer:
30.25π mm^2
Step-by-step explanation:
The area of a circle is π · r^2. simply plug in the radius of 5.5 into "r" and then you square it. Squaring it would result in 30.25. Finally, you multiply it with π. Since you are multiplying two unlike terms, you put the coefficient first and then the variable. The measurements are in millimeters squared so you would have to add them after 30.25π otherwise it would be wrong.
assuming that the curve is banked and the road is frictionless, determine the bank angle with respect to the horizontal.
The bank angle for a frictionless curved road can be calculated using the equations of motion.
The equation of motion for a particle in a curved road is given by F = mgsin(θ) where F is the centripetal force, m is the mass of the particle, g is the acceleration due to gravity and θ is the bank angle. Thus, the bank angle can be calculated by rearranging the equation to θ = arcsin(F/mg). For example, if the mass of the particle is 5kg, the centripetal force is 30N and the acceleration due to gravity is 9.8ms-2, then the bank angle would be θ = arcsin(30/5x9.8) = 20.7°. Thus, the bank angle with respect to the horizontal is 20.7°.
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The area of 755.9ft and 610ft
Answer: 460,874ft^2
Step-by-step explanation:
The area of a rectangle is calculated by multiplying the length by the width. In this case, the length is 755.9ft and the width is 610ft. Therefore, the area of the rectangle is: 755.9ft * 610ft = 460,874ft^2.
I hope this helps :)
what percent of 125 is 250?
what percent of 45 is 9?
what percent of 250 is 100?
what percent of300 is 75?
1) 250÷125=2×100=200%
2) 9÷45= 0.2×100= 20%
3) 100÷250=0.4×100=40%
4) 75÷300=0.214×100=21.4%
How many ways can you make change for 70 cents using only nickel dime and quarters
The number of ways to make a change of 70 cents using only nickel, dime and quarters is given as follows:
15 ways.
How to obtain the number of ways to make the change?The value of each coin is given as follows:
Nickel: $5 cents.Dime: 10 cents.Quarters: 25 cents.Hence the ways to make the change are given as follows:
2 quarters and 2 dimes.2 quarters and 4 nickels.2 quarters, 1 dime and 2 nickels.1 quarter, 1 nickel and 4 dimes.1 quarter, 3 nickels and 3 dimes.1 quarter, 5 nickels and 2 dimes.1 quarter, 7 nickels and 1 dime.7 dimes.6 dimes and 2 nickels.5 dimes and 4 nickels.4 dimes and 6 nickels.3 dimes and 8 nickels.2 dimes and 10 nickels.1 dime and 12 nickels.14 nickels.Which combine to 15 ways.
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It takes Johnny 42 minutes to get to the zoo.After 18 minutes he stopped to get gas for his car .Write an equation to express how many more minutes he had to travel after getting gas
The equation to express how many more minutes he had to travel after getting gas is 42 - 18 = x.
What are the relation between time, distance, and speed?
The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in meters (m) and time is in seconds (s), so the units will be in meters per second (m/s).
The equation to express how many more minutes Johnny had to travel after getting gas is:
42 - 18 = x
Johnny's total travel time to the zoo is 42 minutes
He stopped for 18 minutes to get gas for his car
To find out how many more minutes he had to travel after getting gas, we need to subtract the 18 minutes he spent getting gas from his total travel time.
This is represented by the equation 42 - 18 = x, where x represents the number of minutes he had left to travel after getting gas.
Hence, The equation to express how many more minutes he had to travel after getting gas is 42 - 18 = x.
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so confused
DUE SOON PLEASE HELP IM SO CONFUSED
Answer:
1) Mean = $75812.50
Median = $74000
Mode = $73100
2) Mean = 24.5
Median = 24.33333...
Modal class = 29 - 33
Step-by-step explanation:
Definitions
The mode is the most frequently occurring data value.The median is the middle value when all data values are placed in order of size.The mean is the sum of all data values divided by the total number of data values.Question 1Given data:
71500, 74900, 69700, 82300, 78500, 73100, 73100, 83400Mean
[tex]\begin{aligned}\textsf{Mean}&=\dfrac{71500+74900+69700+82300+78500+73100+73100+83400}{8}\\ &= \dfrac{606500}{8}\\&=75812.50\end{aligned}[/tex]
Median
Place the data values in order of size (smallest to largest):
69700, 71500, 73100, 73100, 74900, 78500, 82300, 83400As there is an even number of data values, the median is the mean of the middle two values:
[tex]\implies \sf Median=\dfrac{73100+74900}{2}=74000[/tex]
Mode
The most frequently occurring data value is $73100. Therefore:
[tex]\implies \textsf{Mode} = 73100[/tex]
Question 2With grouped data, we can only estimate the mean and median.
Mean
To find an estimate of the mean, assume that every reading in a class takes the value of the class midpoint.
The number of days is the frequency (f).
Add a class midpoint (x) and an fx column to the table:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12} \sf Number\;of\;sales&\textsf{Number of days, $f$}&\textsf{Class midpoint, $x$}&fx\\\cline{1-4}\vphantom{\dfrac12}14-18&5&16&80\\\cline{1-4}\vphantom{\dfrac12}19-23&9&21&189\\\cline{1-4}\vphantom{\dfrac12}24-28&6&26&156\\\cline{1-4}\vphantom{\dfrac12}29-33&10&31&310\\\cline{1-4}\vphantom{\dfrac12}\sf Totals&\sum f=30&&\sum fx=735\\\cline{1-4}\end{array}[/tex]
[tex]\textsf{Mean}=\dfrac{\sum fx}{\sum f}=\dfrac{735}{30}=24.5[/tex]
Median
To find an estimate for the median, use linear interpolation.
Add a cumulative frequency column to the table:
[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12} \sf Number\;of\;sales&\textsf{Number of days}&\textsf{Culmulative frequency}\\\cline{1-3}\vphantom{\dfrac12}14-18&5&5\\\cline{1-3}\vphantom{\dfrac12}19-23&9&14\\\cline{1-3}\vphantom{\dfrac12}24-28&6&20\\\cline{1-3}\vphantom{\dfrac12}29-33&10&30\\\cline{1-3}\end{array}[/tex]
Find which class the median is in.
Since n/2 = 30/2 = 15, there are 15 values less than or equal to the median. This means the median must be in the 24-28 class.
Therefore:
[tex]a_1=m-23.5[/tex][tex]b_1=28.5-23.5=5[/tex][tex]a_2=15-14=1[/tex][tex]b_2=20-14=6[/tex]To find the median, m:
[tex]\begin{aligned}\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2} \implies \dfrac{m-23.5}{5}&=\dfrac{1}{6}\\\\ 6(m-23.5)&=5\\\\6m-141&=5\\\\6m&=146\\\\m&=24.3333...\end{aligned}[/tex]
Therefore, the median is 24.3333...
Mode
The modal class is the class with the highest frequency density.
As all the classes are the same width, this is the class with the highest frequency.
Modal class = 29 - 33the principal of a large high school is concerned about the number of absences for students in his school to investigate friends list showing the numbers of absences during the last month of each of the 250
The shape of the sampling distribution of the sample mean is approximately normal because the sample size is greater than 3.
Why do we use sampling distribution?The sampling distribution is the probability distribution of a statistic obtained from a larger sample size drawn from a particular population. The sampling distribution of a certain population is the frequency distribution of a set of possible outcomes for a population statistic.The sampling distribution is the probability distribution of a statistic that is created by drawing several samples from a certain population. Researchers use sample distributions to simplify the statistical inference process.The sampling distribution of a proportion is obtained by repeating your survey or poll for each possible sample of the population. For instance, instead of asking 1,000 cat owners what cat food they like, you could conduct a number of surveys.Given data :
a ) Approximately normal because the sample size is greater than 3.
b ) b ) ux = 1.1 and Jx = = 0.198
c ) c ) P ( ux ∠ 1 ) = normal cdf ( lower : 1000, upper : 1, u : 1.1 , J : 0.198 ) = 0.3068
d ) The principal could pick 50 students may times and find the median and repeat several times until he has every possible sampling distribution.
Completed question :
The principal of a large high school is concerned about the number of absences for students at his school. to investigate, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. for this population of students, the distribution of absences last month is skewed to the right with a mean of 1.1 and a standard deviation of (1.4). suppose that a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated.
a.) What is the shape of the sampling distribution of the sample mean? Explain
b.) What are the mean and standard deviation of the sampling distribution of the sampling mean?
c.) What is the probability that the mean number of absences in a random sample of 50 students is less than 1?
d.) Because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. Describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50.
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There were seven serving lines at the
annual pancake breakfast. The total
number of people served at each of
the seven lines were 126, 118, 127, 134,
98, 132, and 121. What was the median
number of people served?
HELP ASAP! FIND LINEAR EQUATION PARALLEL TO Y = -3/4X + 1 THROUGH POINTS (8,-6)
The equation of the line parallel to y = (-3/4)x + 1 and passing through (8, 6) is y = (-3/4)x
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The slope intercept form of a straight line is:
y = mx + b
Where m is the slope and b is the y intercept.
Two lines are parallel if they have the same slope.
Given the line y = (-3/4)x + 1, the slope is -3/4. The line parallel to y = (-3/4)x + 1 would have same slope of -3/4.
The parallel line passes through (8, -6), hence:
y - y₁ = m(x - x₁)
y - (-6) = (-3/4)(x - 8)
y + 6 = (-3/4)x + 6
y = (-3/4)x
The equation of the line is y = (-3/4)x
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Please help!! :)
In the figure, GH = HI = IJ. Find each length.
a researcher wants to conduct a study to determine whether a newly developed anti-tardy program is successful. two random groups of 100 students each, identified as control and treatment groups, are formed from 200 students who are repeatedly late to school. both groups receive a set of anti-tardy reading materials and a lecture from a teacher and a tardy-reformed student about the negative impacts of being late. in addition, the treatment group also receives materials from the newly developed program. thirty-three of the 100 students in the control and 35 of the 100 students in the treatment group are no longer late to school is recorded 6 months later. use the results to test the hypotheses h0: p1 = p2 and Ha: p1 ? p2 where p1 represents the proportion of students who succeed in the control program and p2 represents the proportion of students who succeed in the newly developed program.
To test the hypotheses h0: p1 = p2 and Ha: p1 ≠ p2, we can use a two-sample proportion test. This test compares the proportion of success (no longer being late to school) in the control group (p1) to the proportion of success in the treatment group (p2) to determine if there is a statistically significant difference between the two proportions.
Here are the steps to perform the test:
State the hypotheses:
h0: p1 = p2 (the proportion of success in the control group is equal to the proportion of success in the treatment group)
Ha: p1 ≠ p2 (the proportion of success in the control group is not equal to the proportion of success in the treatment group)
Select a significance level (alpha): usually, it is set as 0.05
Calculate the test statistic:
p = (p1n1 + p2n2) / (n1 + n2)
z = (p1 - p2) / sqrt(p*(1-p)*((1/n1)+(1/n2)))
Find the p-value:
Using the z-score, look up the probability in a standard normal table.
Make a decision:
Compare the p-value to the significance level. If the p-value is less than or equal to the significance level, then reject the null hypothesis. If the p-value is greater than the significance level, then fail to reject the null hypothesis.
Conclusion:
Interpret the results in terms of the research question. If the null hypothesis is rejected, then the results suggest that there is a statistically significant difference in the proportion of success between the control group and the treatment group
The question is incomplete, the complete question is:
__"'A researcher wants to conduct a study to determine whether a newly developed anti-tardy program is successful. Two random groups of 100 students each, identified as control and treatment groups, are formed from 200 students who are repeatedly late to school. Both groups receive a set of anti-tardy reading materials and a lecture from a teacher and a tardy-reformed student about the negative impacts of being late. In addition, the treatment group also receives materials from the newly developed program. Thirty-three of the 100 students in the control and 35 of the 100 students in the treatment group are no longer late to school is recorded 6 months later.
Use the results to test the hypotheses H0: p1 = p2 and Ha: p1 ≠ p2 where p1 represents the proportion of students who succeed in the control program and p2 represents the proportion of students who succeed in the newly developed program.
What can you conclude using the significance level α = 0.05?""__
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