Answers
Answer:c
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Related Questions
a die is rolled twice and the sum of numbers appearing on the upper faces of them is observed to be 7. what is the probability that the number 2 has appeared atleast once? hint: use the concept of conditional probability)
Answers
The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.
To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.
Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.
Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).
We can use the formula for conditional probability to verify our answer:
P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)
P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)
P(sum is 7) = 6/36 = 1/6
So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.
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Solve for x. Round to the nearest tenth, if necessary. Q R S 75 x 9
Answers
In order to solve for x in this equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3 as the answer. So, x = 8.3.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions, usually containing one or more variables. It is used to describe the relationships between different variables, such as the area of a circle or the slope of a line. Equations can be used to describe the behavior of physical systems, calculate the solutions to problems, and make predictions about future events.
This is happening because when we divide 75 by 9, we are essentially asking "how many 9s go into 75?". 75 divided by 9 is equal to 8.3, meaning 8 and 3/9ths of 9 go into 75. Therefore, x = 8.3.
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In order to solve for x the given equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3. So, x = 8.3.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions, usually involving one or more variables. Used to describe relationships between different variables. Area of circle or slope of line. Equations can be used to describe the behavior of physical systems, calculate solutions to problems, and predict future events.
That's because when you divide 75 by 9, you're essentially asking, "How many 9s are there in 75?" 75 divided by 9 is 8.3. So 3/9 of 8 and 9 is 75. So x = 8.3.
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The complete question is as follows:
Solve for x. Round to the nearest tenth, if necessary.
75 = 9x
simplify the following expression 4 + 4 + 4x
Answers
Answer:
Step-by-step explanation:
8+4x
Solution:
8 + 4x
if you are dealt 4 cards from a standard deck of 52 cards, what is the probability that you will get 3 black cards?
Answers
The probability of getting 3 black cards out of 4 drawn from a standard deck of 52 cards is approximately 0.253 or 25.3%.
To determine the probability of getting 3 black cards out of 4 cards drawn from a standard deck of 52 cards, we can use the hypergeometric distribution.
There are 26 black cards in the deck, and the total number of ways to choose 4 cards from 52 is given by the binomial coefficient C(52, 4). The number of ways to choose 3 black cards out of 26 is given by the binomial coefficient C(26, 3).
The number of ways to choose the fourth card from the remaining 26 non-black cards is given by the binomial coefficient C(26, 1).
Therefore, the probability of getting 3 black cards out of 4 is:
P(3 black cards) = C(26, 3) * C(26, 1) / C(52, 4)
P(3 black cards) = (2600 * 26) / 270725
P(3 black cards) ≈ 0.253
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Describe the pay at the digital source. Use complete sentences and include at least one specific example from the table that you made for part a
Answers
The pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay is represented in dollars per hour, and it ranges from $12 per hour for a new employee in a low-level position to $60 per hour for a senior developer with extensive experience.
For example, if we look at the table created in part a, we can see that a junior developer with less than a year of experience will earn $18 per hour, while a senior developer with more than 10 years of experience will earn $60 per hour. This means that the pay at the Digital Source is directly related to the employee's experience and job position.
Additionally, the table also shows that the pay rate increases as the employee gains more experience and moves up the career ladder. For instance, a junior developer with less than a year of experience will earn $18 per hour, but a mid-level developer with 3-5 years of experience will earn $35 per hour. This shows that employees are rewarded for their skills and experience, and they have the opportunity to advance their careers and earn higher pay rates.
In summary, the pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay rate ranges from $12 per hour to $60 per hour, and it increases as the employee gains more experience and moves up the career ladder. The company values the skills and expertise of their employees and rewards them accordingly.
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Solve for x 8 x + 3 ≥ 19
Answers
Answer:
x ≥ 2
Step-by-step explanation:
8x + 3 ≥ 19
8x ≥ 19 - 3
8x / 8 ≥ 16 / 8
x ≥ 2
Answer:
Sure, I can solve for x:8x + 3 ≥ 19Subtracting 3 from both sides:8x ≥ 16Dividing both sides by 8:x ≥ 2Therefore, the solution is x ≥ 2.
43. 8% complete
Question
The vegetable display automatically sprays a mist over the vegetables according to a repeating timer you set. How many minutes should you set the timer for in order to spray the vegetables 5 times each hour?
A. 15
B. 5
C. 12
D. 20
E. 55
Answers
Option C, 12, is the correct answer. To spray the vegetables 5 times each hour, we need to determine how often the spray should occur.
Since there are 60 minutes in an hour, and we want the vegetables to be sprayed 5 times in that hour, we can divide 60 by 5 to get the interval between each spray:
60 ÷ 5 = 12
This means that the interval between each spray should be 12 minutes. Therefore, we should set the timer for 12 minutes in order to spray the vegetables 5 times each hour.
Option C, 12, is the correct answer.
It is important to note that this assumes the vegetable display is in operation for the entire hour without interruption. If the display is turned off or there are other factors that interrupt the timing, the frequency of sprays may be affected. Additionally, the optimal frequency of sprays may vary depending on the specific vegetables and the environment they are in.
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Need help too figure out these questions these are 2 outa 10 i have too do but these the hardest
Answers
Answer:
1. I don't know
2. 10
Step-by-step explanation:
[tex]c=\sqrt{a^{2}+b^{2} } = \sqrt{6^{2}+8^{2} } = \sqrt{36+64} = \sqrt{100} = 10[/tex]
1) area of shaded area = 14.13 m
area of the remainder of circle = 345.87
2) hypotenuse = 10cm
Step by step
1)
Area of a circle is A=TT r^2
A= (3.14) (6)^2
A= 3.14 x 36
A= 113.04
Now we want to find out just the shaded area
There is 360 degrees in a circle
We are finding 45 degrees of 360 = 1/8
1/8 of 113.04 = 14.13 m
2) hypotenuse is found using formula
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
√100 = √c^2
10 cm = c
A man is trapped in a room at the center of a maze. The room has three exits. Exit 1 leads outside the maze after 3 minutes, on average. Exit 2 will bring him back to the same room after 5 minutes. Exit 3 will bring him back to the same room after 7 minutes. Assume that every time he makes a choice, he is equally likely to choose any exit. What is the expected time taken by him to leave the maze?Hint: Let X = time taken by the man to leave the maze from this room. Let Y = exit he chooses first. So Y belongs in { 1,2,3} Calculate the conditional expectation of time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of time taken to leave the maze.
Answers
The expected time taken by the man to leave the maze is 15 minutes.
To find the expected time taken by the man to leave the maze, we'll first calculate the conditional expectation of time taken given that he chose each of the exits, and then use these conditional expectations to calculate the overall expectation.
Step 1: Calculate the conditional expectations :
- If he chooses Exit 1 (probability 1/3), he leaves the maze after 3 minutes.
- If he chooses Exit 2 (probability 1/3), he returns to the same room after 5 minutes and starts again. So, the expected time in this case is 5 + E(X).
- If he chooses Exit 3 (probability 1/3), he returns to the same room after 7 minutes and starts again. So, the expected time in this case is 7 + E(X).
Step 2: Calculate the overall expectation :
E(X) = (1/3)*(3) + (1/3)*(5 + E(X)) + (1/3)*(7 + E(X))
Now, we'll solve for E(X):
3E(X) = 3 + 5 + 7 + 2E(X)
E(X) = 15 minutes
The expected time taken by the man to leave the maze is 15 minutes.
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According to the problem, there are three possible exits (1, 2, and 3) from the room in the center of the maze. The probabilities of choosing each of these exits are equal.
Exit 1 leads to the outside of the maze, and it takes 3 minutes on average to reach it. Exit 2 leads back to the same room, so the man will need to start over again. Exit 3 also leads back to the same room, and it takes longer than exit 2 to get there (7 minutes).Let X be the time taken by the man to leave the maze from this room. Let Y be the exit he chooses first. Y belongs to {1, 2, 3}. Calculate the conditional expectation of the time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of the time taken to leave the maze.The expected value of X can be calculated as follows:() = ( | = 1) × ( = 1) + ( | = 2) × ( = 2) + ( | = 3) × ( = 3)Expected time to leave the maze through exit 1:( | = 1) = 3Expected time to leave the maze through exit 2:( | = 2) = 5 + ()Expected time to leave the maze through exit 3:( | = 3) = 7 + ()The probability of choosing each exit is 1/3, so:P(Y = 1) = 1/3P(Y = 2) = 1/3P(Y = 3) = 1/3Substituting these values into the equation for ():() = 3(1/3) + (5 + ())(1/3) + (7 + ())(1/3)() = 5 + (2/3)() + (7/3)()() = 15 minutes. Therefore, the expected time taken by the man to leave the maze is 15 minutes.
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2+2+2+2+2+3-3-3-3-21-456--42
Answers
Equations are used in many fields, including physics, engineering, economics, and finance, to model and analyse relationships between variables.
What situation is referred to as an equation?The expressions on either side of the equal sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Solving an equation involves finding the values of the variables that make the equation true.
Two amounts or values are equal when they are stated as so in a mathematical equation, such as 6 x 4 = 12 x 2. two. Noun with a count.
A situation that requires the consideration of two or more elements in order to perceive or comprehend the total situation is referred to as an equation.
[tex]2+2+2+2+2+3-3-3-3-21-456--42 =[/tex]
[tex]2+2+2+2+2+3 = 13[/tex]
[tex]-3-3-3 = -9[/tex]
[tex]-456--42 = -456+42 = -414[/tex]
Therefore,
[tex]2+2+2+2+2+3-3-3-3-21-456--42 = 13 - 9 - 414 = -410[/tex]
Therefore, the value of the expression is [tex]2+2+2+2+2+3-3-3-3-21-456--42[/tex] [tex]= 13 - 9 - 414 = -410[/tex] . As per the given equation.
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please help
At a small animal hospital, there is a 20%
chance that an animal will need to stay
overnight. The hospital only has enough room to
hold animals per night. On a typical day,2 5
animals are brought in.
What is the probability that more than of 2
the animals that are brought in need to
stay overnight?
Answers
The prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
What is binοmial distributiοn?The binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, each with the same prοbability οf success. The distributiοn is characterized by twο parameters: the number οf trials (n) and the prοbability οf success (p) fοr each trial.
Tο sοlve this prοblem, we need tο use the binοmial distributiοn since we have a fixed number οf trials (25 animals brοught in) and each trial (animal) can either be a success (needs tο stay οvernight) οr a failure (dοesn't need tο stay οvernight).
Let X be the number οf animals that need tο stay οvernight. Then X fοllοws a binοmial distributiοn with n = 25 trials and p = 0.2 prοbability οf success (animal needing tο stay οvernight).
We want tο find the prοbability that mοre than 2 animals need tο stay οvernight, which can be expressed as:
nοw, P(X > 2) = 1 - P(X ≤ 2)
Tο calculate P(X ≤ 2), we can use the binοmial cumulative distributiοn functiοn (CDF) οr simply add up the prοbabilities οf X = 0, X = 1, and X = 2:
similarly, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
[tex]= (0.8)^{25} + 25(0.2)(0.8)^{24} + (25\ \text{choose}\ 2)(0.2)^{2}(0.8)^{23}[/tex]
≈ 0.0876
Therefοre, P(X > 2) = 1 - P(X ≤ 2) ≈ 1 - 0.0876 = 0.9124
Sο the prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
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how much work, in foot-pounds, is done when a 50-foot long cable with a weight-density of 8 pounds per foot is wound up 14 feet? do not include any units in your answer.
Answers
The amount of work done when winding up a 50-foot long cable with a weight density of 8 pounds per foot is 14 feet is 5600 foot-pounds.
To explain this answer in more detail, work is a measure of energy and is calculated by multiplying force and distance. In this case, the force is the weight-density of the cable, which is 8 pounds per foot. The distance is the amount of cable that was wound up, which is 14 feet. Multiplying 8 and 14 together gives us the force of 112 pounds. Multiplying 112 by the total length of the cable, which is 50 feet, gives us the answer of 5600 foot-pounds.
To further explain, it is important to remember that 1 foot-pound is equal to 1 pound-foot. That means that 1 pound of force must be applied to move an object 1 foot in order to do 1 foot-pound of work. When this is applied to the example above, we can see that 8 pounds of force must be applied to the cable in order to move it 1 foot. Multiplying this by the length of the cable (50 feet) and the amount of cable wound up (14 feet) gives us the total amount of work done, which is 5600 foot-pounds.
In summary, the amount of work done when winding up a 50-foot long cable with a weight density of 8 pounds per foot is 14 feet is 14 x 8 x 50 = 5600 foot-pounds.
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The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
Answers
= -28
Step by step solved:
Let's assume that the second number is represented by the variable "x".
The sum of the first number (10) and the second number (x) is -18. We can represent this situation with the following equation:
10 + x = -18
To solve for "x", we can isolate the variable by subtracting 10 from both sides of the equation:
x = -18 - 10
Simplifying the right-hand side:
x = -28
Therefore, the second number is -28.
What is the sum of A+C?  a.the matrices b -2,11,5,0,-2,1 c.12,3,1,-2,2,-1 d. -35,28,6,-1,0,12
Answer:on edge B)-2,11,5,0-2,1
Answers
The sum of the matrices A and C from the list of options is the matrix B
Calculating the sum of the matricesGiven the following matrices
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
To find the sum of matrices A and C, we add the corresponding elements in each matrix:
So, we have: A + C
| 0 - 2 6 + 5 2 + 3 |
| 1 - 1 5 - 7 -2 + 3|
Evaluate the sum
| -2 11 5 |
| 0 -2 1 |
This represents option B
Therefore, the sum of matrices A and C is (B)
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Complete question
What is the sum of A+C?
Matrix A
| 0 6 2 |
| 1 5 -2 |
Matrix C
| -2 5 3 |
| -1 -7 3|
how would i do this cause im very lost someone please help
Answers
The decrease in the time spent exercising is 0.74.
Describe Scatter plot?A scatter plot is a type of data visualization that is used to display the relationship between two continuous variables. It consists of a set of data points, each representing an observation, plotted as a point on a two-dimensional graph with one variable on the x-axis and the other variable on the y-axis.
Scatter plots are often used to identify patterns or relationships between two variables, such as correlation or causation. If the points on the plot tend to form a pattern, such as a straight line, then there may be a relationship between the two variables. If the points do not form a pattern, then there may be no relationship between the two variables.
The answers are quite straightforward.
(a) Here, we substitute x=4
(b) Again, we substitute x= 0
(c) Here, if y1=y2-y1= (-0.74x- 0.74+8.54)-(-0.74x + 8.54)= y2-y1= -0.74x- 0.74+8.54 + 0.74x + 8.54= y2- y1= 0.74.
Thus, the decrease in the time spent exercising is 0.74.
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The complete question is
Please help me out! Gonna be posting alot of these so if your good at this stay tuned lol but this is sophomore geometry (not advanced)
Answers
Answer: 63.8
Step-by-step explanation:
-5x - 3y + 7x + 21y Simplify
Answers
Answer:
2x + 18y
Step-by-step explanation:
-5x - 3y + 7x + 21y ----> (combine like terms)
2x - 3y + 21 y ---> (combine like terms)
2x + 18y
Answer:
[tex]\huge\boxed{\sf 2(x + 9y)}[/tex]
Step-by-step explanation:
Given expression:= -5x - 3y + 7x + 21y
Combine like terms= -5x + 7x - 3y + 21y
= 2x + 18y
Common factor = 2So, take 2 as a common factor
= 2(x + 9y)[tex]\rule[225]{225}{2}[/tex]
suppose that iq scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17 . using the empirical rule, what percentage of iq scores are less than 79 ? please do not round your answer.
Answers
Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.
The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.
Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.
Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.
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Suppose the central perk coffee shop sells a cup of espresso for two dollars in a cup of cappuccino for $2. 50 on Friday. Destiny sold 30 more cups of cappuccino then espresso for a total of $178. 50 worth of espresso and cappuccino how many cups of each month old
Answers
Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.
Let's start by defining our variables. Let x be the number of cups of espresso sold and y be the number of cups of cappuccino sold. We know that the price of espresso is $2 per cup and the price of cappuccino is $2.50 per cup. We also know that Destiny sold 30 more cups of cappuccino than espresso and the total sales amount was $178.50.
Using this information, we can create a system of equations to solve for x and y. The first equation comes from the fact that Destiny sold 30 more cups of cappuccino than espresso:
y = x + 30
The second equation comes from the total sales amount:
2x + 2.5y = 178.5
Now we can substitute the first equation into the second equation and solve for x:
2x + 2.5(x + 30) = 178.5
2x + 2.5x + 75 = 178.5
4.5x = 103.5
x = 23
So Destiny sold 23 cups of espresso. Using the first equation, we can find that she sold 53 cups of cappuccino:
y = x + 30
y = 23 + 30
y = 53
Therefore, Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.
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I need help with question 3 I need to find the rate at which the water is rising in cm/seconds
Answers
Answer:
0.01 cm/min
Step-by-step explanation:
The volume of oil in the tank is given by the formula:
V = l × w × h
where l, w, and h are the length, width, and height of the tank respectively.
Substituting the given values, we get:
V = 60 cm × 100 cm × 100 cm = 600,000 cm³
The rate at which the oil is being lost is given as 3.6 litres per hour. Since 1 litre = 1000 cm³, we can convert this to cubic centimeters per hour as follows:
3.6 litres/hour × 1000 cm³/litre = 3600 cm³/hour
To find the rate at which the oil level is falling, we need to divide the rate of oil loss by the surface area of the oil in the tank. Since the tank is rectangular and has a flat bottom, the surface area of the oil is simply the area of the top of the tank, which is:
A = l × w = 60 cm × 100 cm = 6000 cm²
Now, we can calculate the rate at which the oil level is falling as follows:
rate of oil loss ÷ surface area of oil = (3600 cm³/hour) ÷ (6000 cm²)
= 0.6 cm/hour
To convert this to cm/min, we simply divide by 60:
0.6 cm/hour ÷ 60 min/hour = 0.01 cm/min
Therefore, the rate at which the oil level is falling is 0.01 cm/min
Which is not a combination?
(why am i so stuck on this omg)
A. choosing 3 toppings for your pizza
B. lining 3 students up in a row
C. choosing 2 desserts from a tray of 10
D. choosing 5 students to represent a class of 30
Answers
Answer: B
Step-by-step explanation: because
Combine like terms: -4x - 2 - 6x + 8 =
*
Answers
Answer: 21
Step-by-step explanation:because 21 savage is #1
ashley and her brother mason are building block towers. ashley's 1-meter tower is 10 blocks high. mason's tower is only 7 blocks high. if all of the blocks are the same size, how many centimeters taller is ashley's tower than mason's?
Answers
Ashley's tower is 30 centimeters taller than Mason's tower. Ashley's tower is 10 x (1/10) = 1 meter tall. Mason's tower, on the other hand, is 7 x (1/10) = 0.7 meters tall.
Ashley's tower is 10 blocks high and each block has a height of 0.1 meters since 1 meter is divided into 10 equal parts. Therefore, the total height of Ashley's tower is 10 x 0.1 = 1 meter. Mason's tower, on the other hand, is 7 blocks high and has a total height of 7 x 0.1 = 0.7 meters. The difference between Ashley's tower and Mason's tower is the height of Ashley's tower minus the height of Mason's tower, which is 1 meter - 0.7 meters = 0.3 meters. To convert meters to centimeters, we need to multiply by 100, so Ashley's tower is 0.3 x 100 = 30 centimeters taller than Mason's tower.
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mathematics homework
Answers
Answer:
Step-by-step explanation:
(g * h)(24)
gh*24
24gh
The figure below is composed of a regular hexagon and three congruent triangles. What is the area of the figure rounded to the nearest square meter?
Answers
The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.
Describe regular pentagon?With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.
Regular pentagons have a number of distinctive features, including:
A regular pentagon has 108 degree internal angles that are all equal.
A standard pentagon's outside angles are all 72 degrees in angle.
A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.
Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.
First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:
s = r * √(3)
where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:
s = 5 * √(3)
simplifying, we get:
s ≈ 8.7 meters
Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:
A = (1/2) * b * h
where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:
h = (1/2) * s * √(3)
Plugging in the value for s, we get:
h ≈ 7.5 meters
Now we can calculate the area of one of the triangles:
A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters
Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:
A = 6 * (s²) * √(3)/4 + 3 * A
Plugging in the values we calculated, we get:
A ≈ 96.9 square meters
Rounding to the nearest square meter, we get:
A ≈ 97 square meters
Therefore, the answer is A. 97 m².
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2. (2 points) a state administered standardized reading exam is given to eighth grade students. the scores on this exam for all students statewide have a normal distribution with a mean of 538 and a standard deviation of 30. a local junior high principal has decided to give an award to any student who scores in the top 2.5% of statewide scores. how high should a student score be to win this award? round your answer up to the next integer.
Answers
A student should score 598 in order to win the award.
To calculate how high should a student score be to win this award, we use the z-score formula.
z=(x-μ)/σ
Where,
μ= Mean of the scores on this exam
σ= Standard deviation of the scores on this exam
z= Z-score
x= Scores on this exam
By substituting the given values in the formula, we get
z=(x-μ)/σ
[tex]= (x-538)/30[/tex]
To find the highest 2.5%, we use the normal distribution table which gives us the Z-score corresponding to 0.975. The highest 2.5% is on each side of the normal distribution curve. Therefore, we have to subtract the area from the highest score, then divide by two.
Subtracting 0.975 from 1 gives us the area to the left of this point on the table which is equal to 0.025.Z = 1.96.
So the score should be one standard deviation above the mean. Thus, the score a student needs to get in the top 2.5% of statewide scores is
[tex]Z = (x - 538) / 30[/tex]
[tex]1.96 = (x - 538) / 30x - 538 = 1.96 * 30x - 538 = 58.8 + 538x = 597.8[/tex]
The score a student needs to get in the top 2.5% of statewide scores is 598, rounded up to the next integer.
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Match the term with the definition: The length of the line through the center of a circle that touches two points on the edge of the circle. a) Radius b) Circumference c) Diameter d) Tangent Line
Answers
Diameter
Which is the following is correct?
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The expressions 6 × 3+6 × 8 and 6(3 + 8), respectively, indicate the combined size of the two rooms.
What is a Plane figure's overall area?A plane figure's overall area is the sum of all of the distinct area shapes that make up that plane figure.
We have two regions that take on the characteristics of a rectangle based on the information provided.
The office area = 18 square feet
There are 48 square feet in the sitting room.
The two chambers now have a combined size of 18 + 48 = 66 square feet.
Now, the expressions that better represent the total area of the two rooms can be written as 6 × 3+6 × 8 and 6(3 + 8).
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Find the X
geometry
pt.2
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The angle of x in the given circle is 51 degrees.
What is theorem of secant and tangent line in circle?In the case when a tangent line and a secant line originate from the same external point, the mean of the exterior angle is equal to half the difference between the major arc and the minor arc that are created by the tangent and secant lines.
From the given figure we observe that the secant line and tangent line start from the same exterior angle.
Thus, according to the theorem of secant and tangent line of circle we have:
angle x = (DA - DB) /2
angle x = (178 - 76) / 2
angle x = 102 /2
angle x = 51 degrees.
Hence, the angle of x in the given circle is 51 degrees.
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original sample: 84, 71, 79, 96, 87. do the values given constitute a possible bootstrap sample from the original sample?
Answers
Yes, the given values constitute a possible bootstrap sample from the original sample.
Bootstrap samples are taken with replacement from the original data set. In other words, it means that each sample consists of a random sample of the same size as the original data set taken from the original data set.
Hence, a given set of values can be a bootstrap sample from the original sample as long as the values are randomly selected from the original sample and with replacement.
The sample is said to be a bootstrap sample from the original data set if it satisfies the following properties:
1. The bootstrap sample must be of the same size as the original data set.
2. Each observation from the original data set must have an equal chance of being selected in each bootstrap sample.3. The bootstrap samples must be independent of each other.
In the given problem, the sample consists of 5 values, namely 84, 71, 79, 96, and 87.
These values can be a bootstrap sample from the original sample as long as the values were randomly selected with replacement from the original sample.
Since the problem does not provide any information on how the sample was obtained, it cannot be determined whether or not it is a bootstrap sample.
Therefore, the answer is that the given values constitute a possible bootstrap sample from the original sample.
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