The R. Davis children are preparing for a relay event in which they will compete in a 1/3 mile relay race. The opening round of the competition will include three kids who will compete in the race.
This means that in the relay event, each kid will have to run 1/9th of a mile. Students will need to improve on their speed, endurance, and coordination in order to prepare for the race. They must be able to effortlessly deliver the baton from one runner to another, maintain their speed throughout the race, and push themselves to the maximum. In addition to physical preparation, students must improve their mental focus and motivation. They will do so. need to stay positive and motivated throughout the race, and work as a team to achieve their goals.
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What is the scenario for R. Davis students in the relay tournament? How many students will run in the first round of the tournament, and what is the distance they will cover?
suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?
New car prices to fall within is $18,300 - $41,900
Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.
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Find the area of the following
rhombus:
10 cm
6 cm
8 cm
A = [?] cm²
Answer:96
Step-by-step explanation:
[tex]Area=\frac{d1 d2}{2}[/tex]
[tex]Area=\frac{(6+6)(8+8)}{2}[/tex]
[tex]Area=96[/tex]
vhat is the volume of the composite figures
104 ft³
120 ft³
150 ft³
160 ft³
Based on the attached figure, the volume of the composite figure is 408 cm³
Calculating the volume of the figureA composite figure is a three-dimensional shape that is made up of two or more simpler shapes.
To find the volume of a composite figure, you need to break it down into its simpler shapes and then use the appropriate formulas to calculate the volume of each individual shape
The volume of the composite figure is:
Volume = area of base * height
Substituting:
Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm
So, we have
Volume = area of base * height = 68 cm² * 6 cm = 408 cm³
This means that
The volume is 408 cm³
Hence, the volume is 408 cm³
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A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. 2 1 The equation of the regression line is Y - 2+0.98 40 30 . A browsing time of 17 minutes is found to result in an amount spent of 40.3 dollars. What is the predicted amount spent? Ex: 7.9 dollars 20 . 10 Where is the observed value in relation to the regression line? Pick 0 10 20 40 50 dollars Pick Browsing time in minutes) A browsing time of 14 minutes is found to result in a amount spent of 10.84 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? A browsing time of 28 minutes is found to result in a amount spent of 27.2 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? dollars ✓ Pick above below 2 on Check Next
EXPLANTION:
1. For a browsing time of 17 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X, where X is the browsing time in minutes.
Step-by-step:
Y = 2 + 0.98(17)
Y = 2 + 16.66
Y = 18.66 dollars
The observed value (40.3 dollars) is above the regression line, as it is higher than the predicted amount spent (18.66 dollars).
2. For a browsing time of 14 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(14)
Y = 2 + 13.72
Y = 15.72 dollars
The observed value (10.84 dollars) is below the regression line, as it is lower than the predicted amount spent (15.72 dollars).
3. For a browsing time of 28 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(28)
Y = 2 + 27.44
Y = 29.44 dollars
The observed value (27.2 dollars) is below the regression line, as it is lower than the predicted amount spent (29.44 dollars).
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the vertices of a triangle are A(8,-24) B(8,-8) C(16,-8). If the triangle is dilated by a scale factor of 1/4 what will be the coordinates of C
After the triangle is dilated by a scale factor of 1/4, the coordinates of point C' are (10, -14).
How to find the coordinates ?We can use the following formula to find the coordinates of point C' after the triangle has been dilated by a scale factor of 1/4:
C' = (1/4)(C - center) + center
where C denotes the original coordinate of point C and centre denotes the dilation center (which is not specified in the problem).
However, because this is the most common choice and is not explicitly stated, we can assume that the center of dilation is the midpoint of line segment AB. Line segment AB's midpoint is:
((8+8)/2, (-24-8)/2) = (8, -16)
So, in the formula, we can substitute this value for Centre:
C' = (1/4)(C - (8, -16)) + (8, -16)
All that remains is to plug in the coordinates of point C and simplify:
C' = (1/4)((16, -8) - (8, -16)) + (8, -16)
= (1/4)(8, 8) + (8, -16)
= (2, 2) + (8, -16)
= (10, -14)
As a result, the coordinates of point C' after the triangle has been dilated by a factor of 1/4 are (10, -14).
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Psychologists are concerned that ____ personality tests are not easy to interpret and do not always produce consistent results because they are not standardized.
Psychologists have raised concerns about the accuracy and validity of ____ personality tests, as they are not standardized. This means that the same test administered to two different people can yield different results, making it difficult to interpret. Moreover, results may be inconsistent, meaning the same test administered at different times could produce different results. This lack of consistency can lead to inaccurate interpretations and can render the tests less useful. Furthermore, there is a lack of standardization of criteria and methodologies used to evaluate personality tests, which could lead to misinterpretations of results.
In order to address these issues, it is important to use standardized personality tests, which are tested and validated to ensure consistent and accurate results. This will ensure that the tests yield consistent results and can be interpreted accurately.
Additionally, researchers must adhere to established guidelines and criteria to ensure that the results are reliable and valid. This will enable professionals to confidently use the tests and make accurate interpretations of the results.
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solve the inequality -8x < 32 should it be reveresed
The value of x for the given inequality to justify the equation to get the desired result of the equation is x < - 4 .
Define inequality:
In mathematics, inequality refers to a statement that compares two values or expressions, indicating that one value or expression is greater than or less than the other. An inequality can be represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). For example, "2x + 3 > 5" is an inequality that states that the expression "2x + 3" is greater than "5". Inequalities are often used in algebra, calculus, and other branches of mathematics to represent relationships between variables or to solve equations.
What about equation in the relation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two expressions, separated by an equals sign "=" and it states that the value of one expression is equal to the value of the other expression. The expressions in an equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used in many areas of mathematics to describe relationships between variables, to solve problems, and to make predictions. For example, the equation "x + 3 = 7" states that the value of the expression "x + 3" is equal to "7".
According to the given information:
For the following equation we have that,
⇒ - 8x < 32
⇒ -x < [tex]\frac{32}{8}[/tex]
⇒ -x < [tex]4[/tex]
⇒ x < [tex]- 4[/tex]
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a rod placed up against a wall is sliding down. the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. when this distance is 152 inches, how fast is the distance between the bottom of the rod and the foot of the wall changing? the rod is 172 inches long.
when the distance between the top of the rod and the foot of the wall is 152 inches, the distance between the bottom of the rod and the foot of the wall is decreasing at a rate of approximately 19.08 inches per second.
In this case, we are given that the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. We want to find the rate at which the distance between the bottom of the rod and the foot of the wall is changing.
We can start by using the Pythagorean theorem to relate the three distances involved: the height of the rod (h), the distance between the top of the rod and the foot of the wall (x), and the distance between the bottom of the rod and the foot of the wall (y). Specifically, we have:
[tex]h^2 = x^2 + y^2[/tex]
To find the rate at which y is changing, we can take the derivative of both sides of this equation with respect to time (t), using the chain rule:
2h dh/dt = 2x dx/dt + 2y dy/dt
We are given that dh/dt = -9 inches per second (since h is decreasing). We also know that h = 172 inches and x = 152 inches (when y = 0). Substituting these values and solving for dy/dt, we get:
dy/dt = (h/x) * (dx/dt - (x/y) * dh/dt)
dy/dt = (172/152) * (-9 - (152/y) * 9)
dy/dt = -19.08 inches per second (rounded to two decimal places)
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x° = ½ • (30 + 2x – 30)
Simplifying the expression resulted to x° = x
How to solve for xThe expression x° = ½ • (30 + 2x – 30) can be simplified as follows:
The term 30 - 30 simplifies to 0, so we can remove it from the expression:
x° = ½ • (30 + 2x - 30)
x° = ½ • (2x)
We can simplify the fraction ½ by dividing the numerator by the denominator:
x° = x
Therefore, the solution to the equation x° = ½ • (30 + 2x – 30) is x = x°. In other words, any value of x is equal to its corresponding value in degrees.
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the australian sheep dog is a breed renowned for its intelligence and work ethic. it is estimated that 45% of adult australian sheep dogs weigh 65 pounds or more. a sample of 12 adult dogs is studied. what is the mean number of dogs who weigh 65 lb or more?
5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.
We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:
p = 0.45
Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.
The formula for X's mean or expected value is:
E(X) = np
When we change the values of n and p, we obtain:
E(X) = 12(0.45) = 5.4
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You must find the sum of the volume of the square prism and the square pyramid.
Enter the letter of the answer.
The sum of the volume of the square prism and the square pyramid is 672 cubic inches.
What is prism ?
A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.
According to the question:
First, let's calculate the volume of the square prism:
The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:
V_prism = lwh = 10 x 10 x 6 = 600 cubic inches
Next, let's calculate the volume of the square pyramid:
The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:
[tex]B = b^2 = 6^2 = 36 square inches[/tex]
The height of the pyramid is also 6 inches, so we have:
V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches
Finally, the total volume is the sum of the volumes of the prism and pyramid:
V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches
Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.
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match the quadratic equation with the easiest method that could be used to find the solutions.
The quadratic equation with the easiest method that could be used to find the solutions:
5x² + 24x + 21 = 0 :: Factoring
x² + 4x + 27 = 0 :: Completing the Square
x² + 8x + 15 = 0 :: Factoring
-3x² = -5x + 8 :: Dividing by x and simplifying gives Quadratic Formula
What is equation?An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of an equation is to solve for the variable(s) that make the equation true.
Here,
The easiest method to find the solutions of a quadratic equation depends on the form of the equation and the tools available. Here are some common methods and when they are typically used:
Zero Product Property/Factoring: This method is used when the quadratic equation can be factored into two linear factors, each of which equals zero.
Square Root Property: This method is used when the quadratic equation is in the form of x² = a, where a is a positive number. For example, the equation x² = 9 can be solved using the Square Root Property: take the square root of both sides and remember to include both the positive and negative roots, giving x = ±3.
Completing the Square: This method is used when the quadratic equation is in the form of x² + bx + c = 0, where b and c are constants. Completing the square involves adding and subtracting a constant term to both sides of the equation to create a perfect square trinomial, which can then be factored and solved using the Square Root Property.
Quadratic Formula: This method is used when the quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a.
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This quarter, a local gym has 759 members. That is 65% more than it had last quarter, due to a change in rates. How many members were there last quarter?
Answer:
759=165% of last quarters members so you could divide by 1.65(move the decimal place twice to the left) so you get 460 people were there last quarter
Step-by-step explanation:
justin recently drove to visit his parents who live 420 miles away. on his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). if justin spent a total of 12 hours driving, find the two rates (in mph). round your answer to two decimal places, if needed.
Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.
Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.
By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:
Time is a function of both speed and distance.
Similar to how long it would take Justin to drive back home:
Time is a function of distance and speed (x - 24)
Justin drove for a total of 12 hours, so we can construct the following equation:
420/x + 420/(x-24) = 12
By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:
[tex]x^2 - 24x - 840 = 0[/tex]
We can find the value of x by using the quadratic formula:
[tex]x = (24 +- \sqrt{(242 + 41840)}) / 2[/tex] or x = -18
We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.
We can confirm the following to see if the solution is accurate:
420/42 + 420/18 = 10 + 23.33 = 33.33
Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.
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Which of the following proportions is true?
16/36 = 12/27
4/16 = 2/14
15/20 = 24/36
12/15 = 47/50
Answer:
16/36 = 12/27
Help me find the slope of the line for each one it’s ok if you don’t know all of them
Answer:
1. 1/2
2. -4/1
3. 1/1
Step-by-step explanation:
Answer:
1 y=2/1+2
2 y=.25x+3
3 y=x-2
Step-by-step explanation:
Step-by-step
y=mx+b
1. 2
2. .25
3. 1
Tolosa sold 540 eggs if these are 35% of total eggs,then how many eggs are not sold?
The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
To find the number of eggs that are not sold, we can subtract the number of eggs sold from the total number of eggs:
1542 - 540 = 1002
Find out more about The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
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help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex] .
What dimensions are expressed in linear units?The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that [tex]ZF = ZD + DF = 24 + 28 = 52[/tex] and [tex]FH = ZG = 30 and ZH = 36.[/tex]
As a result, Fard ZH's perimeter is as follows:
perimeter = [tex]= ZF + FH + ZH + ZG[/tex]
perimeter [tex]= 52 + 30 + 36 + 30[/tex]
perimeter [tex]= 148[/tex]
So the perimeter of Fard ZH is [tex]148[/tex] .
(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:
[tex]V = (xB - xA, yB - yA)[/tex]
Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.
Plugging in the given values, we get:
[tex]V = (5 - 10, 2 - 14)[/tex]
[tex]V = (-5, -12)[/tex]
Therefore, The V's direction is [tex](-5, -12)[/tex] .
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Triangle ABC is graphed.
Answer: 2+2
Step-by-step explanation: easy thanks :)
construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place. n=5, s=4.4, c=0.95
Therefore, the 95% confidence interval for the population standard deviation is approximately (2.6, 12.3).
To construct a 95% confidence interval for the population standard deviation, we will use the chi-square distribution. Here are the steps:
Step 1: Identify the given values.
n = 5 (sample size)
s = 4.4 (sample standard deviation)
c = 0.95 (confidence level)
Step 2: Find the degrees of freedom.
df = n - 1 = 5 - 1 = 4
Step 3: Find the chi-square values.
For a 95% confidence interval, we will use the values corresponding to 2.5% and 97.5% in the chi-square distribution table. For df = 4:
Chi-square (0.025) = 11.143
Chi-square (0.975) = 0.485
Step 4: Calculate the confidence interval for the population variance.
Lower limit:[tex] (n - 1) * s^2 / Chi-square (0.025) = 4 * (4.4)^2 / 11.143 = 6.960[/tex]
Upper limit:[tex] (n - 1) * s^2 / Chi-square (0.975) = 4 * (4.4)^2 / 0.485 = 151.977[/tex]
Step 5: Calculate the confidence interval for the population standard deviation by taking the square root of the variance limits.
Lower limit: [tex]√6.960 = 2.6[/tex]
Upper limit:[tex] √151.977 = 12.3[/tex]
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PLEASE HELP ME if you you thank you so much! I need all calculations to receive full credit
Answer:
The television tower is 132 feet high.
Step-by-step explanation:
Let h be the height of the television tower. Set up and solve this proportion.
[tex] \frac{3}{5} = \frac{h}{220} [/tex]
[tex]5h = 660[/tex]
[tex]h = 132[/tex]
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Find a point e satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5].
c =
The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697
How to solve mean value theorem?The conclusion of the Mean Value Theorem says that there is a number
c in the interval (1, 5) such that:
f'(c) = (f(5) - f(1))/(5 - 1)
We are given the function f(x) = x⁻⁸
Thus:
f(1) = 1⁻⁸ = 1
f(5) = 5⁻⁸ = 0.00000256
Thus:
f'(c) = (0.00000256 - 1)/4
= -0.25
f'(c) = -8x⁻⁹
Thus:
-8c⁻⁹ = -0.25
c⁻⁹ = 0.25/8
c⁻⁹ = 0.03125
c = 0.03125^(-1/9)
c = 1.4697
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ziggy has an exercise blood pressure of 150/60, a heart rate of 140 bpm, a max vo2 of 33 ml/kg/min, and a stroke volume of 95 ml. what is her mean arterial pressure?
90 mm Hg is Zigg's mean arterial pressure.
Here's the formula for calculating MAP: MAP = (CO x SVR) + CVPR
where:
CO stands for cardiac output (measured in liters per minute).
SVR stands for systemic vascular resistance (measured in mm Hg/L/min).
CVPR stands for central venous pressure (measured in mm Hg).
Now, let's get started with the calculation of MAP.
First, let's calculate CO (cardiac output): CO = HR x SV
where:
HR is heart rate (measured in beats per minute).
SV is stroke volume (measured in milliliters per beat).
CO = 140 bpm x 95 mlCO = 13300 ml/minCO = 13.3 L/min
Next, we need to calculate SVR (systemic vascular resistance).
The formula for calculating SVR is: SVR = (MAP - CVP) / CO
where:
MAP is mean arterial pressure (measured in mm Hg).
CVP is central venous pressure (measured in mm Hg).
CO is cardiac output (measured in liters per minute).
Since we don't have CVP in this question, let's assume it to be zero.
SVR = (MAP - 0) / 13.3 L/minSVR = MAP / 13.3 L/min
Now, we can rearrange the above equation to calculate
MAP:
MAP = SVR x 13.3 L/minMAP = 60 mm Hg (diastolic pressure) + 1/3 (systolic pressure - diastolic pressure)MAP = 60 mm Hg + 1/3 (150 mm Hg - 60 mm Hg)MAP = 60 mm Hg + 30 mm HgMAP = 90 mm Hg
Therefore, Ziggy's mean arterial pressure (MAP) is 90 mm Hg.
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out of 230 racers who started the marathon, 211 completed the race, 12 gave up, and 7 were disqualified. what percentage did not complete the marathon? round your answer to the nearest tenth of a percent.
the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.
To find the percentage of racers who did not complete the marathon, we need to divide the number of racers who did not complete by the total number of racers and then multiply by 100 to get a percentage.
Number of racers who did not complete = 12 + 7 = 19
Total number of racers = 230
Percentage of racers who did not complete = (19/230) x 100% = 8.3%
Therefore, the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.
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You're playing a game in which the probability of winning each round is. 20.
On average, how many rounds do you have to play to first win?
Answer: You would probably have to play about 10 rounds.
A tortoise is walking in the desert. It walks for 6.4 meters at a speed of 4 meters per minute. For how many minutes does it walk?
Answer:
1.6 minutes
Step-by-step explanation:
6.4 meters/4 speed
the following frequency distribution displays the weekly sales of a certain brand of television at an electronics store. number sold frequency 01-05 12 06-10 5 11-15 5 16-20 5 21-25 25 how many weeks of data are included in this frequency distribution?
There are 52 weeks of data included in this frequency distribution.
The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store.
We need to find the number of weeks of data included in this frequency distribution.From the given data, we can see that the frequency column represents the number of televisions sold per week.
To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:12 + 5 + 5 + 5 + 25 = 52
Therefore, there are 52 weeks of data included in this frequency distribution.
The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store. We need to find the number of weeks of data included in this frequency distribution.
From the given data, we can see that the frequency column represents the number of televisions sold per week. To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:
12 + 5 + 5 + 5 + 25 = 52
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the marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. what is the probability that a class of 36 has an average midterm mark that is more than 77.83?
The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.
Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)
P(x > 77.83) = 1 - P(x < 77.83)
P(x > 77.83) = 1 - 0.9234
P(x > 77.83) = 0.0766
What is the slope of the line on the graph?
Options:
A) 1/2
B) 2
C) -1/2
D) -2
Answer:
Slope is -2. So, choice D is the best option.
Step-by-step explanation:
Start with one point then use the formula to get to the next point:
Rise
------
Run
Let's start at (0,5) then count down 2 points, which is the "Rise"(seems like an interesting name to pick but it works).
Next, you go to the right once. Which counts as the "Run".
Remember: The slope is like a ratio, and the "y" will always go as the numerator and the "x" as the denominator. Which is why "Rise" is on top and the "Run" is on the bottom.
So your answer would be 2/1. And that simplifies to 2. But since you went down and not up, it would be negative 2.
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Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score isAttitudes toward school. The Survey of Study
Habit= 127.8.
(a) Assuming that ? = 30 for the population of older students, carry out a test of
H0: ?= 115
H0: ?> 115
Report the P-value of your test, and state your conclusion clearly.
(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of ? is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?
(a) To test the hypotheses H0: µ = 115 and H1: µ > 115, we will conduct a one-sample t-test using the given information.
Step 1: Calculate the t-value.
t = (sample mean - population mean) / (standard deviation / √sample size)
t = (127.8 - 115) / (30 / √25)
t = 12.8 / 6
t = 2.13
Step 2: Determine the degrees of freedom (df).
df = sample size - 1
df = 25 - 1
df = 24
Step 3: Find the P-value.
Using a t-table or calculator, find the P-value corresponding to t = 2.13 and df = 24. The P-value is approximately 0.022.
Step 4: State the conclusion.
Since the P-value is less than the commonly used significance level of 0.05, we reject the null hypothesis (H0: µ = 115) and conclude that the mean score for older students is significantly higher than the mean score for the entire population.
(b) The two important assumptions for the t-test are:
1. The sample is randomly selected from the population.
2. The population is normally distributed.
The most important assumption for the validity of the conclusion in part (a) is the normality of the population. If the population is not normally distributed, the results of the t-test may not be valid, and the conclusion may be inaccurate.
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