The equation of the perpendicular line is y = (7/3)x - 2/3. And the slope of the line is 7/3.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
y = -(3/7)x + 4
The equation of the line that is perpendicular to y = -(3/7)x + 4 will be given as,
y = (7/3)x + d
The equation passes through (2, 4) will be given as,
4 = (7/3) × 2 + d
c = - 2/3
Then the equation of the perpendicular line is given as,
y = (7/3)x - 2/3
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what is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?
The rate of change in the farm's average tree height in feet in relation to the number of years the trees have been planted is 7 ft/yr.
Given that,
In the picture we have a table with the linear relationship between the average height in feet of tree on a form and the number of years since tree where planned.
We have to find what is the rate of change in the farm's average tree height in feet in relation to the number of years the trees have been planted.
We know that,
1,3,6,11,15 years have passed since the trees were planted.
10, 24, 45, 80, 10 is the average height in feet.
The number of years since the trees were planted as a whole is now 1+3+6+11+15 = 36.
Total Average Height (ft.) = 10 + 24 + 45 + 80 + 108=267
Therefore, the rate of change in average height is equal to the sum of average height and the number of years.
The average height change rate is 267 divided by 36.
The average height is changing at a rate of 7.4 feet every year.
Average height change of less than 7 feet each year.
In relation to the number of years since the trees were planted, the average annual growth rate of the farm's trees, measured in feet, is 7 ft/yr.
Therefore, The rate of change in the farm's average tree height in feet in relation to the number of years the trees have been planted is 7 ft/yr.
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Point (25,125) means that the monthly home heating bill was $
for an average monthly temperature of
°F.
The point (25,125) means that the monthly home heating bill was $5 for an average monthly temperature of 1°F.
How to interpret the meaning of the point?From the question, we have the following parameters that can be used in our computation:
Point (25, 125)
This point can be expressed as
(x, y) = (25, 125)
The average monthly temperature bill is then calculated using the following equation
Average monthly temperature bill = y/x
Substitute the known values in the above equation, so, we have the following representation
Average monthly temperature bill = 125/25
Evaluate
Average monthly temperature bill = 5
Hence, the average monthly temperature = 5
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The graph of a function f(x) passes through the following points: (0, 2), (1, 0), ( – 1,0) Which of the following could be f(x)?
A possible definition for function f(x) is given as follows:
y = -2x² - 2.
How to define the function f(x)?According to the Factor Theorem, the function f(x) can be defined according to it's zeros, as follows:
f(x) = a(x - x')(x - x'').
In which:
a is the leading coefficient.x' and x'' are the zeros of the function.Two of the points of the function are (1,0) and (-1,0), hence the zeros are given as follows:
x' = 1, x'' = -1.
Then the function can be defined as follows:
f(x) = a(x - 1)(x + 1)
f(x) = a(x² - 1).
When x = 0, y = 2, hence the leading coefficient a is obtained as follows:
2 = a(0 - 1)
-a = 2
a = -2.
Thus the complete definition of the function is of:
y = -2(x² - 1)
y = -2x² - 2.
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Someone help me please ASAP please
Plot a scatter graph to represent the data.
Draw the line of best fit.
What type of correlation is shown? How are mass of a cake and cooking time related?
divide user number by down numbers
Step-by-step explanation:
lowest volume was achieved in sample 1 where the highest cake volume was shown in sample 5. Table 4 shows the sensory scores reported by sensory 60 panellists of a 1-9 point scale using a hedonic rating to evaluate the overall acceptability of the cake samples. The overall acceptability was affected significantly (p<0.05) for wheat flour in the cake samples as shown in Table 5. The highest value was 8.3 achieved in sample 6 where the lowest value was 6.8 found in sample 1 while the average of overall acceptability is 7.55 which mean the medium between like moderately
Penny earned a 74% on her first test. If each test has 100 points, what must she earn on her next test to achieve an average of at least 80%?
Step-by-step explanation:
the mean value is average is the sum of all data divided by the number of data points.
with the second test she will have 2 data points.
the first was 74 points (74% of 100 points = 74 points).
x = 2nd test result
(74 + x)/2 = 80
74 + x = 160
x = 86
she must earn 86% on her second test to achieve an average score of 80%.
Two crew of highway worker are repaving a highway. Crew 1 ha 6 worker and Crew 2 ha 8 worker. In 4 day of work, Crew 1 repaved 2 mile of the highway. In 5 day of work, Crew 2 repaved 3 mile of the highway. Select all the tatement that are true. Repone
Crew 1 worked a total of 12 worker-day. Crew 1 worked a total of 12 worker-day. Crew 1 repaved the highway at a rate of12mile per day. Crew 1 repaved the highway at a rate of 1 2 mile per day. Crew 2 repaved the highway at a fater rate than Crew 1. Crew 2 repaved the highway at a fater rate than Crew 1. Crew 1 required more worker-day per mile than Crew 2. Crew 1 required more worker-day per mile than Crew 2. Crew 2 repaved the highway at a rate of 1313worker-day per mile
Crew 1 more worker-days to repave the same distance, it is also clear that they required more worker-day per mile than Crew 2.
True. Crew 1 worked a total of 12 worker-day.
True. Crew 1 repaved the highway at a rate of 12 mile per day.
True. Crew 2 repaved the highway at a faster rate than Crew 1.
True. Crew 1 required more worker-day per mile than Crew 2.
True. Crew 2 repaved the highway at a rate of 1.3 worker-day per mile.
Crew 1 - 6 workers and 4 days of work = 24 worker-days to repave 2 miles of highway. This means that Crew 1 repaved the highway at a rate of 12 miles per day.
Crew 2 - 8 workers and 5 days of work = 40 worker-days to repave 3 miles of highway. This means that Crew 2 repaved the highway at a rate of 1.3 worker-days per mile.
Since Crew 2 repaved the highway in fewer worker-days, it is clear that they repaved the highway at a faster rate than Crew 1. Additionally, since it took Crew 1 more worker-days to repave the same distance, it is also clear that they required more worker-day per mile than Crew 2.
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Mr. Torre tell hi cla that when they have completed the aignment, they may read. Eleven tudent are reading, which i about 40
The students that still need to complete their assignments = 14
According to the given question,
The total number of students in Mr. Torres's class = 24
Now as the question tells us,
Mr. Torres instructed the students to read only if they have finished their assignments.
The percentage of the class that is reading = is 40% which means that 40% of the class has completed their assignments.
Now we have to calculate the number of students that are still doing their assignments,
⇒ 40 % of the 24
⇒ [tex]\frac{40}{100}[/tex] x 24
⇒ 0.4 x 24
⇒ 9.6 ≈ 10
So the students that have completed their assignments = 10
Students that are still doing their assignments,
⇒ 24 - 10
⇒ 14
Therefore, The students that still need to complete their assignments = 14
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Mr. Torres tells his class of 24 that when they have completed their assignment they may read at the end of class 40% of the class is reading how many students still need to complete their assignment
the f-test for anova in a regression model with 4 predictors and 47 observations would have how many degrees of freedom?
The degree of freedom for the f-test for anova in a regression model with 4 predictors and 47 observations is (4,42)
degree of freedom = (k, n - k - 1)
= (4, 47 - 4 - 1)
= (4, 42).
Any statistical test with an F-distribution for the test statistic under the null hypothesis is known as an F-test. In order to determine which statistical model better represents the population from which the data were sampled, it is most frequently applied when contrasting models that have been fitted to data sets.
Exact "F-tests" are typically required after least squares fitting of the models to the data. In honor of Ronald Fisher, George W. Snedecor came up with the name. In the 1920s, Fisher created the statistic as the variance ratio.
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lanson biked 1 13/14 miles to the library, the. 1 4/9 miles to the park. how far did he bike altogether
Answer: 3 47/126
Step-by-step explanation: You have to find the common denominator to make the problem easy and make sense. I highly recommend using a fraction calculator if you aren't sure how to do it.
You tie a spherical balloon that is 2 feet in diameter to a
stake in the ground. The string is 15 feet long. The wind
blows and you observe that the top of the balloon is
8 feet over from the stake, as shown in the diagram.
What is the height, b, of the balloon?
Show your work.
15 ft
2 ft
8 ft
Answer:
Step-by-step explanation:
What is the scale factor from the map to the actual community center Iready level G
HELP PLS
The scale factor from the map is 1 in : 8 ft
How to determine the scale factor of dilation?From the question, we have the following parameters that can be used in our computation:
Kitchen = 3 in
Also from the question, we have the following legend/key
1 in : 8 ft
The above represents the scale factor of dilation used on the map
This can be re-expressed as
Scale = 1 in : 8 ft
Hence, the scale factor of dilation is 1 in : 8 ft
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Solve the system of inequalities.
-7x+3y ≤ 15
6x-5y<12
The inequalities for the equation -7x + 3y ≤ 15 is [tex]x\ge \frac{-15+3y}{7}[/tex] and 6x - 5y < 12 is [tex]x < \frac{12+5y}{6}[/tex]
What is inequalities ?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Inequality of wealth (the distribution of wealth across households or individuals at a particular point in time), inequality of opportunity (the impact on income of circumstances over which individuals have no control, such as the availability of jobs), and lifetime inequality (the inequality in incomes for an individual over his or her lifetime) are all related concepts.
- 7x ≤ 15 - 3y
(-7x)(-1) ≥ 15 (-1) - 3y(-1)
7x ≥ -15 + 3y
Dividing by 7 we get
[tex]x\ge \frac{-15+3y}{7}[/tex]
6x < 12 + 5y
Dividing by 6 we get
[tex]x < \frac{12+5y}{6}[/tex]
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For the same samples statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. Choose the correct answer below.a. 99%, because as the level of confidence increases, Zc increases.b. 99%, because as the level of confidence increases, Zc decreases.c.90%, because as the level of confidence decreases, Zc increases.d. 90%, because as the level of confidence decreases, Zc decreases.
The 99% confidence level produces the most comprehensive interval due to the increase in critical value.
99%, because, as the level of confidence increases, zc increases.
The level of confidence is the probability that actual value will fall in the confidence interval determined using sample statistics. As the probability increases, the area (middle part) under the curve expands, which results in increasing the critical value(zc) that determines the acceptance region.
The increase in the critical value results in increasing the margin of error, which defines the confidence interval's spread from the mean value of the distribution.
Hence, the 99% confidence level produces the most comprehensive interval due to the increase in critical value.
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What is the expression in rational exponent form? (∜8³)⅓
Answer:
2 is the answer
Step-by-step explanation:
(∜8³)⅓
the (⁴√8) is 2 { 2×2×2×2 = 8}
= (2³)⅓
= 2³×⅓
= 2
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Please help me I’m struggling
The percentage of 12-month-old baby boys who weigh is 0.5.
What is mean and standard deviation?
The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.Z-scores are calculated using the formula z = (x-μ)/σ, where x represents the raw score, the population mean, and the population standard deviation. The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates.Mean=22.5; Standard deviation=2.2
The z-score for the given weight is
z−score = Blood pressure reading−Mean / Standard deviation
= 23.6−22.5/2.2
= 1.1/2.2
=0.5
Hence, the percentage of 12-month-old baby boys who weigh is 0.5
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What is an equation for the line that passes through the points (4,8) and (-2,-7)?
john is moving from portland to sacramento, which is 600 miles away. he is traveling at an average speed of 55 miles per hour. jon stops for gas after a couple of hours and wonders how much further he needs to go. if y represents distance from sacramento and x represents time, which linear equation would indicate the amount of miles jon still has to travel to sacramento? a.) y equals short dash 55 x plus 600 b.) y equals short dash 600 x plus 55 c.) y equals 55 x minus 600 d.) y equals 600 x minus 55
Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
Hence, Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
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Which point represents the number 2?
The number 2 is at point ___
Answer:
Point C
Step-by-step explanation:
a problem in your textbook asked you to look at five versions of the number 3 which were displayed at different orientations and identify which were backwards. the point of the demonstration was that:
The point of the demonstration was to illustrate that numbers are not always represented in the same way, and can look different when rotated or flipped. It also showed that numbers can look the same, even when they are not in the same orientation.
The demonstration asked the student to examine five different versions of the number 3. Each version was displayed in a different orientation. The point of the demonstration was to illustrate that numbers are not always represented the same way. Each number can look different when rotated or flipped. It also showed that numbers can look the same, even when they are not in the same orientation. This helps to show that numbers have an orientation and can be presented in different ways. It also helps to demonstrate that numbers are not always read from left to right, but can be read from right to left as well.
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Find the average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds.
The average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².
What is the average acceleration?Acceleration is the amount by which the velocity of something changes over a set period of time.
The formula to find the acceleration is a=(v-v₀)/t, where a=average acceleration, v=final velocity, v₀=initial velocity and t=time.
Given that, final velocity =14.2 m/s, initial velocity=0 and t=22.8 seconds.
Now, the average acceleration is
a=(14.2-0)/22.8
= 14.2/22.8
= 0.62 m/s²
Therefore, the average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².
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what is the f-statistic for the f-test for joint significance for the variables that are omitted between regression 1 and regression 2?
The F-statistic for the F-test for joint significance for the variables that are omitted between Regression 1 and Regression 2 is calculated by dividing the difference between the sum of squares of the two regressions by the sum of squares of the omitted variables.
The F-statistic for the F-test for joint significance is a measure of the strength of the relationship between the variables that have been omitted between two regressions. It is calculated by taking the difference between the sum of squares of the two regressions, and dividing it by the sum of squares of the omitted variables. This gives us a value that indicates how well the omitted variables explain the variance in the data. If the value is high, then the omitted variables do explain a significant amount of the variance in the data, indicating that they should not be omitted.
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Applications of Basic Equations:
97.) An isosceles triangle has two congruent sides that measure 3x + 8 in. and - 9x-5 over 2 in. respectively. The third sidle
28 over 2y-1
measures in. If the perimeter of the triangle is 72 in., find the length of all three sides. Find the value of y. Hint:
solve for x first.
Answer:
Step-by-step explanation:
Let the congruent sides of an isosceles △ be x.
Let the base of the isosceles △ be y
According to the 1st condition,
x+x+y=30
2x+y=30
According to the 2nd condition
x=y+3
x−y=3
Solving equation (1) and (2)
2x+y=30
x−y=3
-------------------
3x=33
x=
3
33
x=11
By substituting x=11 in equation (1)
2x+y=30
2(11)+y=30
22+y=30
y=30−22
=8
∴ The length of the sides of a △ are 11cm,11cm and 8cm.
what is the probability a randomly selected 30 year old in 1970 earned more than his or her parents at age 30?
In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-is The probability is. 83
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
How is probability determined?
picture for "probability"
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
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in the athletics team, tall members tend to win three times as many medals as short members. this year the team has won 60 medals so far. how many of these have been won by short athletes?
in the athletics team, tall members tend to win three times as many medals as short members.20 number of medals have been won by short athletes.
This question can be solved by using the ratio method. Since tall athletes are said to win three times as many medals as short athletes, this means that the ratio of tall athletes' medals to short athletes' medals is 3:1. We can use this ratio to calculate how many medals have been won by short athletes. Since the team has won a total of 60 medals, we can divide this number by 4 (the total number of medals in the ratio) to get 15. We then multiply 15 by the ratio of short athletes' medals (1) to get 15 medals. This means that short athletes have won 20 medals, since 15 multiplied by 3 is 45, leaving 60-45=15 medals for the short athletes. Thus, 20 medals have been won by short athletes.
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a bridge hand consists of 13 cards dealt at random from the deck of 52. the probability that a bridge hand will have exactly 2 queens is:
The probability that a bridge hand will have exactly 2 queens is 0.45%.
To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:
P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n is the total number of trials
k is the number of successes in the trials
p is the probability of success in a single trial
In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).
Plugging these values into the formula, we get:
P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹
= (78) * (1/169) * (4/13)¹¹
= (4/169) * (4/13)¹¹
This simplifies to:
P(exactly 2 queens) = (4/169) * (4/13)¹¹
= (4/169) * (4/169)¹¹
= (4/169)¹²
The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.
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Find the measure of ∠QTS.
Image posted !! Please help giving brainliest for whoever gets it right
Step-by-step explanation:
Given that,QTR =77°
RTS =71°
QTS=QTR+RTS
=77°+71°
=148°
Answer:
∠QTS is 148°
Step-by-step explanation:
To find the measure of ∠QTS we would simply add the angles.
[tex]77+71=148[/tex]
The sum of interior angles in a triangle is 180°
We can check our work by subtracting the adjacent angles from 180.
A right angle is 90°.
[tex]90-77=13[/tex]
[tex]90-71=19[/tex]
[tex]180-13-19=148[/tex]
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Coefficient of x^5 in expansion of (2x-1)^6
The coefficient x⁵ in expansion of (2x - 1)⁶ is; -192
How to solve Binomial expansion?We are given the expression;
(2x - 1)⁶
Using Pascals triangle, the coefficient of the terms here are;
1 6 15 20 15 6 1
The general formula for binomial expansion is;
(x + y)ⁿ = ⁿC₀xⁿy⁰ + ⁿC₁xⁿ⁻¹y¹ + ⁿC₂xⁿ⁻²y²+......+ ⁿCₙx⁰yⁿ
Thus, we can find the expansion of (2x - 1)⁶ as;
1[(2x)⁶ * (-1)⁰] + 6[(2x)⁵ * (-1)¹] + 15[(2x)⁴ * (-1)²] + 20[(2x)³ * (-1)³] + [15(2x)² * (-1)⁴] + [6(2x)¹ * (-1)⁵] + [1(2x)⁰ * (-1)⁶]
= 64x⁶ - 192x⁵ + 240x⁴ - 160x³ + 60x² - 12x + 1
The coefficient we are looking for is -192
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PLEASE HELP ASAP, 100 POINTS FOR ANSWER
6.For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles
7.For the Raleigh company write an equation in slope-intercept form to represent the amount charged, y, for x number of miles.
8.For the Raleigh company write an equation in point-slope form to represent the amount charged, y, for x number of miles for the company in Raleigh, NC.
9. Write an equation in standard form to represent the amount charged, y, for x number of miles for the company in Raleigh.
10.What does the slope mean in the context of the problem?
6) A table that represents the cost of the cab ride is;
5 15.25
10. 28.95
15. 42.45
20. 55.95
7) The equation in slope intercept form is;
y = 2.70x + 1.95
8) The equation in point slope form is; y - 15.25 = 2.70(x - 5)
9) The equation in standard form is; -2.70x + y = 1.95
10) What the slope indicates is the amount of money charged per mile driven by each cab ride.
How to express a linear equation?6) A table that represents the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20.
5 15.25
10. 28.95
15. 42.45
20. 55.95
7) The general equation of a line in slope intercept form is y = mx + b
where;
m is slope.
b is y-intercept
The slope will be 2.70 since that is how much we go up for a mile
Similarly, 1.95 is y-intercept since it is where we start no matter what and we have to add that constant fee every time.
Thus, the equation is;
y = 2.70x + 1.95
8) The general equation for a line in point slope form is;
y - y₁ = m(x - x₁)
Thus, the equation by taking the first coordinate is;
y - 15.25 = 2.70(x - 5)
9) The equation in standard form will be;
y = 2.70x + 1.95
Thus;
-2.70x + y = 1.95
10) What the slope indicates is the amount of money charged per mile driven by each cab ride.
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Select the correct answer from each drop-down menu.
Consider absolute value function f.
f(x) = -x + 4|
The vertex of the function is a
V
at
The vertex of the absolute value function f(x) = (-2/3)*|x + 4| is:
(-4, 0)
Which is the vertex of the absolute value function?Here we have the following absolute value function:
f(x) = (-2/3)*|x + 4|
The x-value of the vertex is the one that makes the argument of the absolute value part equal to zero, so we will get:
x + 4 = 0
x = -4
To et the y-value of the vertex we evaluate the function in x = -4, we will get:
f(-4) = (-2/3)*|-4 + 4|
f(-4) = 0
Then the vertex of the absolute value function is (-4, 0).
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Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.
What percentage to the nearest hundredth of children are born from pregnancies lasting more than 274 days?
What percentage to the nearest hundredth of children are born from pregnancies lasting less than 246 days?
Answer:
Step-by-step explanation:
Use the formula for a normal dist.
⊕ = sigma
∪ = standard deviation, mu
f(x) = 1 / (⊕*[tex]\sqrt{2\pi }[/tex])*e^(-1/2*(x-∪/⊕)^2)
A) f(274) = 1 / (16*[tex]\sqrt{2\pi }[/tex])*e^(-1/2*(274-266/16)^2)
= 0.022
B F(246) = 1 / (16*[tex]\sqrt{2\pi }[/tex])*e^(-1/2*(246-266/16)^2)
= 0.017