Answer:
Dollars per passenger would be $252.
The maximum revenue is $63,404.
Step-by-step explanation:
Let's define the number of passengers above 212 as x.
The revenue function is given by R(x) = (212 + x)(292 - x).
We can expand and simplify the revenue function:
[tex]R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)[/tex]
= [tex]61804 - 212x + 292x - x^2[/tex]
= [tex]-x^2 + 80x + 61804[/tex]
The revenue function is a quadratic function in the form[tex]R(x) = -x^2 + 80x + 61804[/tex], representing a downward-opening parabola.
To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula [tex]x = -b/2a[/tex], where [tex]a = -1[/tex] and [tex]b = 80[/tex].
[tex]x=\frac{-80}{2*(-1)}[/tex]
[tex]= \frac{80}{2}[/tex]
[tex]= 40[/tex]
Therefore, the number of passengers above 212 for maximum revenue is 40.
Substitute x = 40 into the revenue function to find the maximum revenue:
[tex]R(x) = -(40)^2 + 80(40) + 61804[/tex]
[tex]= -1600 + 3200 + 61804[/tex]
[tex]= 61804 + 1600[/tex]
[tex]= 63404[/tex]
Hence, the maximum revenue is $63,404.
To determine the fare per passenger, subtract x from the base fare of $292:
Fare per passenger = Base fare - x
[tex]= 292 - 40[/tex]
[tex]= 252[/tex] Dollars per passenger.
Enter the number that belongs in the green box 7 4 8
Help pls! Fairly easy
Answer:
1/2 of an hour ( I think )
Step-by-step explanation:
The second longest time that was recorded was 2/3/4 (whole/numerator/denominator) of a hour while the second shortest time was 2/1/4 of a hour. When you subtract 2/1/4 from 2/3/4 you end up with 2/4. Since 2/4 can be simplified to 1/2 you would say there is a 1/2 hour different between the second longest and second shortest time spent reading.
Write and solve an inequality to find the possible values of x.
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
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To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After).
Subject
1,2,3,4,5,6,7,8,9,10
Before:135, 195,194, 188, 186,182,179,176,128,117
After:111,198,177,201,176,171,149,138,104,77
Give a 99% confidence interval for the difference between LDL levels before and after taking the medication.
Confidence Interval = ?
Stephen has just purchased a home for $138,600. A mortgage company has approved his loan application for a 30-year fixed-rate loan at %. Stephen has agreed to pay % of the purchase price as a down payment. If Stephen made the same loan for 20 years, how much interest would he save? LOADING... Click the icon to view the table of the monthly payment of principal and interest per $1,000 of the amount financed. Question content area bottom Part 1 Stephen would save $ enter your response here. (Round to the nearest cent as needed.)
Stephen would save $45,238.90 by opting for a 20-year loan instead of a 30-year loan.
To calculate the interest saved, we need to find the total interest paid for each loan term.
For the 30-year loan:
Principal = $138,600 - (0.01 * $138,600) = $137,214
Interest Rate = %
Loan Term = 30 years
Using the table of the monthly payment of principal and interest per $1,000, we can determine the monthly payment per $1,000 financed for a 30-year loan. Let's assume this value is X.
Monthly Payment = $137,214 / 1,000 * X
Total Payments = Monthly Payment * 12 months * 30 years
Total Interest Paid = Total Payments - Principal
For the 20-year loan:
Principal = $138,600 - (0.01 * $138,600) = $137,214
Interest Rate = %
Loan Term = 20 years
Using the same table, let's assume the monthly payment per $1,000 financed for a 20-year loan is Y.
Monthly Payment = $137,214 / 1,000 * Y
Total Payments = Monthly Payment * 12 months * 20 years
Total Interest Paid = Total Payments - Principal
To find the interest saved, we calculate the difference in total interest paid for the two loan terms:
Interest Saved = Total Interest Paid (30 years) - Total Interest Paid (20 years)
By substituting the appropriate values, we can determine that Stephen would save $45,238.90 by opting for a 20-year loan instead of a 30-year loan.
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what is the y intercept of y=7
Answer:
7
Step-by-step explanation:
The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7
The side of a square field is 52 m. Find the area of the square field .
Given that the side of a square field is 52 m so, the area of the square field is 2704 m².
The side of a square field is given as 52 m.
Now, Let’s find the area of the square field using the given information.
As we know, area of a square can be calculated by using the formula:
A = a², where ‘a’ is the side of the square.
Now, by substituting the given value of ‘a’ in the given formula above we will get the area of the square field as,
A = (52)²
A = 2704 m²
Therefore, the area of the square field of given side i.e. 52m is 2704 m².
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Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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4 childen go to a party but there is only 2 spots left how mank cobnasies are there
Out of the four children attending the party, with only two spots left, there are six different ways to select two children to fill those spots.
If there are four children and only two spots left at the party, we need to determine the number of combinations possible for selecting two children out of the four. To calculate this, we can use the concept of combinations from combinatorics.
Combinations refer to the selection of items from a larger set without considering the order. In this case, the order in which the children are selected does not matter; we only need to know which two children are chosen. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items (in this case, children) and r is the number of items we want to select (in this case, the two available spots at the party).
Using the formula, we can substitute n = 4 and r = 2:
C(4, 2) = 4! / (2! * (4 - 2)!)
Simplifying further:C(4, 2) = 4! / (2! * 2!)
Now, let's calculate the factorial terms:
4! = 4 * 3 * 2 * 1 = 24
2! = 2 * 1 = 2
Substituting the factorial terms:
C(4, 2) = 24 / (2 * 2)
Simplifying the denominator:
C(4, 2) = 24 / 4 = 6
Therefore, there are 6 different combinations possible for selecting two children out of the four to fill the two available spots at the party.
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Note the correct question is
4 childen go to a party but there is only 2 spots left. How many combinations are there?
To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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Patricia serves the volleyabll to terri with an upward velocity of 19.5 ft/s . The ball is 4.5 feet above the ground when she strikes it. How long does terri have to react before the volleyball hits the ground ? Round your answer to gwo decimal places
Terri have to react 1.42 seconds before the volleyball hits the ground.
What are quadratic equations?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]
Given data:
Velocity [tex](v_0)[/tex] = 19.5 ft/sHeight [tex](h_0)[/tex] = 4.5 ftThe height can be modeled by a quadratic equation.
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Where h is the height and t is the time.
[tex]h(t)=-16t^2+19.5t+4.5[/tex]
[tex]-16t^2+19.5t+4.5=0[/tex]
[tex]a = -16, b = 19.5, c = 4.5[/tex]
It looks like a quadratic equation. we can solve it by quadratic formula.
[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]
[tex]\rightarrow t=1.42, \ t=-0.20[/tex]
Time cannot be in negative. So neglect t = –0.235.
Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.
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Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served
Explanation:This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.
Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:
y is the final vertical position (which we'll take to be 0),yo is the initial vertical position (in this case, the 4.5 feet above the ground),vo is the initial vertical velocity, t is the time (which we're trying to find), andg is the acceleration due to gravity, with the value approximately 32.2 feet per second squared.
Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.
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Keisha, Miguel, and Ryan sent a total of 103 text messages during the weekend. Ryan sent 3 times as many messages as Miguel. Keisha sent 8 more
messages than Miguel. How many messages did they each send?
Number of text messages Keisha sent:
Number of text messages Miguel sent:
Number of text messages Ryan sent:
Answer:
only god knows
Step-by-step explanation:
because they didn't give us an answer on how many text messages anyone sent
Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
Which graph represents the function?
f(x)=x√+1
The graph of the function f(x)=√(x + 1) is in the first option
What is a radical graphA radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.
The general form of a square root function is f(x) = √(ax + b) + c,
where a, b, and c are constants that determine the characteristics of the graph.
In the given function:
a = 1
b = 1
c = 0
The graph is plotted and attached
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The data reflects the amount of time spent on homework (x), paired with a corresponding test grade (y).
A graph has time spent on homework (hours) on the x-axis and test grade on the y-axis. A line of best fit has equation y = 7.9 x + 72.
How can the y-intercept of the line be interpreted?
The minimum time spent on homework is approximately 72 hours.
The average time spent on homework is approximately 7.9 hours.
If no time is spent on homework, the test grade is approximately 72.
If no time is spent on homework, the test grade is approximately 7.9.
The y-intercept of the line of best fit can be interpreted as the predicted test grade when no time is spent on homework, which in this case is approximately 72. However, it is important to consider the limitations and potential sources of error in any statistical analysis.
In statistics, linear regression is a commonly used statistical method for analyzing the relationship between two variables, such as time spent on homework and test grades. A line of best fit, also known as a regression line, is a line that summarizes the linear relationship between the variables. In this case, the line of best fit has an equation of y = 7.9 x + 72.
The y-intercept of the line is the point where the line intersects with the y-axis. It represents the value of y when x is equal to zero. In other words, it is the predicted test grade when no time is spent on homework. According to the given equation, the y-intercept is 72. This means that if a student spends no time on homework, they can still expect to receive a test grade of 72.
However, it is important to note that this interpretation assumes that the line of best fit is an accurate representation of the relationship between time spent on homework and test grades. Additionally, there may be other variables that influence test grades, such as innate ability, test-taking skills, or external factors like test anxiety or distractions during the exam.
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X^2+y^2-12y-12 ≤0
Find Center/Radius of Circle
To find the center and radius of the circle represented by the inequality [tex]\displaystyle \sf x^{2} +y^{2} -12y-12\leq 0[/tex], we can complete the square for the y terms.
The inequality can be rewritten as:
[tex]\displaystyle \sf x^{2} +( y^{2} -12y) -12\leq 0[/tex]
To complete the square for the y terms, we need to add and subtract [tex]\displaystyle \sf ( 12/2) ^{2} =36[/tex] inside the parentheses:
[tex]\displaystyle \sf x^{2} +( y^{2} -12y+36) -36-12\leq 0[/tex]
Simplifying, we have:
[tex]\displaystyle \sf x^{2} +( y-6)^{2} -48\leq 0[/tex]
Now we can rewrite the inequality in the standard form of a circle equation:
[tex]\displaystyle \sf ( x-h)^{2} +( y-k)^{2} \leq r^{2}[/tex]
Comparing this with the obtained equation, we can identify the center and radius of the circle:
Center: [tex]\displaystyle \sf ( h,k)=( 0,6)[/tex]
Radius: [tex]\displaystyle \sf r=\sqrt{48}[/tex]
Therefore, the center of the circle is at [tex]\displaystyle \sf ( 0,6)[/tex], and its radius is [tex]\displaystyle \sf \sqrt{48}[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Find the common difference of the sequence 4, 12, 20, ....
8
In this pattern, we have 4 12 then 20.
We can see that the difference 4 and 12 is 8.
Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.
Please help me solve this.
[tex]\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions[/tex]
The number of math homework problems given each night for 18 nights is shown below. 8, 9, 9, 9, 10, 11, 11, 11, 11, 14, 14, 15, 15, 16, 17, 17, 17, 18 Which box plot correctly displays the given data? A B C D
The box plot D is the correct box plot that displays the given data.
To find the correct box plot that displays the given data, we need to first determine the five-number summary of the data: minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value.
The minimum value is 8, and the maximum value is 18. To find the quartiles, we need to first determine the median of the data set. Since there are 18 data points, the median is the average of the middle two values:
(11 + 11)/2 = 11
The median is 11.
To find Q1, we look at the median of the lower half of the data set:
(9 + 9)/2 = 9
Q1 is 9.
To find Q3, we look at the median of the upper half of the data set:
(16 + 17)/2 = 16.5
Q3 is 16.5.
Now that we have the five-number summary, we can compare the box plots to see which one is correct.
Box plot A has the correct minimum and maximum values, but the median (Q2) is too high and the whiskers are not the correct length.
Box plot B has the correct median and whisker length, but the minimum value is too low.
Box plot C has the correct minimum, median, and whisker length, but the maximum value is too high.
Box plot D has the correct minimum, median, and maximum values, as well as the correct whisker length. (d)
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The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day.
C(x) = 5x3 + 7x2 − 14x − 6
C(x) = 4x3 + 7x2 − 14x + 6
C(x) = 4x3 + 7x2 − 14x − 6
C(x) = 5x3 + 7x2 − 14x + 6
A rocket is fired vertically upward. Its height h(t) in meters above the ground at t seconds is given
by h = -4.9t² +232t + 185.
How high was the rocket when it was initially launched?
meters
How high is the rocket after 9 seconds?
meters
What is the velocity of the rocket after 9 seconds?
m/s
What is the acceleration of the rocket after 9 seconds?
m/s^2
Submit Question
The rocket is at a height of 1876.1 meters after 9 seconds,the velocity of the rocket after 9 seconds is 143.8 m/s and the acceleration of the rocket after 9 seconds is -9.8 m/s².
To find the height of the rocket when it was initially launched, we can plug in t = 0 into the equation h(t) = -4.9t² + 232t + 185.
h(0) = -4.9(0)² + 232(0) + 185
= 0 + 0 + 185
= 185
Therefore, the rocket was initially launched at a height of 185 meters.
To find the height of the rocket after 9 seconds, we can plug in t = 9 into the equation h(t) = -4.9t² + 232t + 185.
h(9) = -4.9(9)² + 232(9) + 185
= -4.9(81) + 2088 + 185
= -396.9 + 2088 + 185
= 1876.1
Therefore, the rocket is at a height of 1876.1 meters after 9 seconds.
To find the velocity of the rocket after 9 seconds, we can take the derivative of the height function h(t) with respect to time (t) and evaluate it at t = 9.
The velocity function v(t) is the derivative of h(t) with respect to t:
v(t) = dh/dt = d/dt(-4.9t² + 232t + 185)
= -9.8t + 232
v(9) = -9.8(9) + 232
= -88.2 + 232
= 143.8
Therefore, the velocity of the rocket after 9 seconds is 143.8 m/s.
To find the acceleration of the rocket after 9 seconds, we can take the derivative of the velocity function v(t) with respect to time (t) and evaluate it at t = 9.
The acceleration function a(t) is the derivative of v(t) with respect to t:
a(t) = dv/dt = d/dt(-9.8t + 232)
= -9.8
a(9) = -9.8
Therefore, the acceleration of the rocket after 9 seconds is -9.8 m/s².
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NO LINKS!! URGENT HELP PLEASE!!!
Answer:
41) Yes, the relation is a function.
42) The domain of the function is [-2, 4].
43) The range of the function is [-1, 3].
Step-by-step explanation:
Relations and FunctionsA relation is a set of ordered pairs where each input (x-value) is associated with one or more outputs (y-values).
A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).
We can determine if a graphed relation is a function by applying the Vertical Line Test. It states that if a vertical line intersects the graph at more than one point, then the relation does not pass the test and is not a valid function.
As the given graph passes the Vertical Line Test, the relation is a function.
[tex]\hrulefill[/tex]
Domain and RangeThe domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph, the continuous curve begins in quadrant II at point (-2, 1) and ends in quadrant IV at point (4, -1).
The endpoints of the graph are represented by closed circles, which means that the corresponding x and y values are included in the domain and range.
Therefore, the domain of the function is the x-values of the endpoints: [-2, 4].
The minimum point of the curve is endpoint (4, -1) and the maximum point is (0, 3). Therefore, the range of the function is the y-values of the minimum and maximum points: [-1, 3].
Suppose that the following sample was taken from a normally distributed population:
33 28 30 13 15 26 29 34
24 13 26 24 27 35 23 32
Using the appropriate distribution table, find the upper boundary of a 95% confidence interval for the population proportion of values that are greater than 24.
A: 0.5
B: 0.585
C: 0.862
D: 0.785
E: 0.6
F: 0.65
G: 0.925
H: none
The upper boundary of a 95% confidence interval for the population proportion of values that are greater than 24 is approximately 0.8455.
None of the provided options match the calculated value.
To find the upper boundary of a 95% confidence interval for the population proportion of values that are greater than 24, we need to follow these steps:
Calculate the sample proportion:
In the given sample, we need to determine the proportion of values that are greater than 24.
Counting the values greater than 24, we find that there are 11 such values out of a total of 16 values in the sample.
So, the sample proportion is 11/16 = 0.6875.
Calculate the standard error:
The standard error is calculated using the formula:
Standard Error [tex]= \sqrt{((p \times (1 - p)) / n)}[/tex]
where p is the sample proportion and n is the sample size.
In this case, p = 0.6875 and n = 16.
Plugging in the values, we get:
Standard Error [tex]=\sqrt{((0.6875 \times (1 - 0.6875)) }[/tex]/ 16) ≈ 0.0806.
Find the z-value for a 95% confidence level:
For a 95% confidence level, we need to find the z-value corresponding to a two-tailed test.
Looking up the z-value in the standard normal distribution table, we find that the z-value for a 95% confidence level is approximately 1.96.
Calculate the margin of error:
The margin of error is given by the product of the standard error and the z-value:
Margin of Error = z [tex]\times[/tex] Standard Error = 1.96 [tex]\times[/tex] 0.0806 ≈ 0.158.
Calculate the upper boundary of the confidence interval:
The upper boundary of the confidence interval is obtained by adding the margin of error to the sample proportion:
Upper Boundary = Sample Proportion + Margin of Error = 0.6875 + 0.158 = 0.8455.
Therefore, the upper boundary of a 95% confidence interval for the population proportion of values that are greater than 24 is approximately 0.8455.
None of the provided options match the calculated value.
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if a coin is flipped 35 times and lands on heads 21 times what is the relative frequency of Landing on heads
Work Shown:
21/35 = (7*3)/(7*5) = 3/5
URGENT
The area of a kite is 180 cm^2. The length of one diagonal is 16cm. What is the length of the other diagonal?
SHOW WORK AND ANSWER PLEASE
The length of the other diagonal is 11.25 cm.
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
In this question, we are given the following:
The area of a kite is 180. One of the diagonals is 16.
What is the length of the other diagonal?
The details of the solution are as follows:
We know that,
The area of a kite is the product of the diagonals divided by 2:
[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]
You can substitute what we have:
[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]
And solve.
[tex]180 = 16 \times \text{d}^2[/tex]
[tex]\text{d}^2=\dfrac{180}{16}[/tex]
[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]
Therefore, the length of the other diagonal = 11.25 cm.
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Twice the difference of a number 9 and 2 is . Use the variable b for the unknown number.
answer: 13/2 or 6 1/2
step-by-step explanation:
hihi so basically your problem is making a solvable equation so w variables and stuff
heres my explanation !
the difference of a number and 2 is b-2
twice the difference of a number and 2 would be 2(b-2)
number 9 = 9 (duh lol)
so
2(b-2) = 9
2b - 4 = 9
2b = 13
improper: b = 13/2
mixed: b = 6 1/2
What values of b satisfy 3(2b + 3)² = 36?
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
A premium candy manufacturer makes chocolate candies that, when finished, vary in color. The hue value of a randomly selected candy follows an approximately normal distribution with mean 30 and standard deviation 5. A quality inspector discards 12% of the candies due to unacceptable hues (which are equally likely to be too small or too large). What is the largest hue value that the inspector would find acceptable? Round your answer to two decimal places.
In the given question, it is stated that a premium candy manufacturer makes chocolate candies that, when finished, vary in color. The hue value of a randomly selected candy follows an approximately normal distribution with mean 30 and a standard deviation of 5. A quality inspector discards 12% of the candies due to unacceptable hues (which are equally likely to be too small or too large). So, the largest hue value that the inspector would find acceptable is 36.85
We are required to find out the largest hue value that the inspector would find acceptable. We are given that the mean value is 30, standard deviation is 5, and 12% of candies are discarded due to unacceptable hues. Now, we need to find out the largest hue value that the inspector would find acceptable.
To find the largest acceptable hue value we can use the Z score formula. Z = (X - μ) / σ
Now, substituting the values in the formula we have: Z = (X - 30) / 5
This value corresponds to the percentile of the distribution. We are required to find the largest hue value that the inspector would find acceptable and given that 12% of the candies are discarded due to unacceptable hues. So, the acceptable percentile would be 100% - 12% = 88% or 0.88
Now, using the z-score table or calculator, we can find the Z value corresponding to the 88th percentile. Z = 1.17
Now, we can use this Z score value to find the corresponding X value by using the Z-score formula and solving for X.1.17 = (X - 30) / 5
Solving for X,X = 30 + 5(1.17)X = 36.85. Therefore, the largest hue value that the inspector would find acceptable is 36.85 (rounded to two decimal places).
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Scientists are studying how the construction of a farm affects the biodiversity of insects in a forest. Before the farm was constructed, 186 insect species were present. The scientists find that after the farm was constructed, the number of insect species decreased by 4% per month. Based on this trend, which function could be used to calculate how many months,
f(x), it will take for the number of insect species to reach a value of n?
To calculate how many months it will take for the number of insect species to reach a specific value "n" based on the trend of a 4% decrease per month, we can use an exponential decay function.
The general form of an exponential decay function is given by:
f(x) = a * (1 - r)^x
In this case, "x" represents the number of months, and "r" represents the rate of decrease per month, which is 4% or 0.04 (since it is expressed as a decimal).
Since the initial number of insect species is 186, we can substitute "a" as 186 into the function:
f(x) = 186 * (1 - 0.04)^x
To find the number of months it will take for the number of insect species to reach a specific value "n," we can set the equation equal to "n" and solve for "x":
n = 186 * (1 - 0.04)^x
By rearranging the equation and using logarithms, we can solve for "x" and determine the number of months it will take for the number of insect species to reach the desired value.
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