To construct a histogram of the estimates and compare it to the above estimates, follow these steps:
1. Compile the data and organize it into groups or bins.
2. Assign each group a height or frequency, usually the number of occurrences in the group.
3. Represent each group by drawing a bar with the corresponding height.
4. Connect the tops of the bars to form a histogram.
Comparing the histogram to the above estimates, if the histogram is similar in shape and spread, then the estimates are consistent.
The best estimate of the random modifier without examining the value is the mode of the data, which is the value that occurs most often.
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a runner wants to run 11.7 km . she knows that her running pace is 6.7 mi/h .how many minutes must she run
The number of minutes she must run to reach her goal is 65.1 minutes.
The time she must run for is found by dividing the distance by the speed:
Time = Distance / Speed
We need to convert the distance from kilometers to miles before substituting values into the formula.
11.7 km = 11.7 / 1.609344 = 7.270043 miles
The formula now becomes:
Time = 7.270043 miles / 6.7 mi/h
Time = 1.085081 h
To get the time in minutes, we need to convert the time in hours to minutes. There are 60 minutes in an hour, so there are
Time = 1.085081 h x (60 minutes/1 hour)
Time = 65.104863 minutes = 65.1 minutes
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Find the compound interest and the total amount after eight years if the interest is compounded every two years.
Principal = ₹10,000
Rate of interest = 20%
Total amount = (find)
Total interest = (find)
After 8 years, the total amount is ₹38,416 and the compound interest is ₹28,416.
What is the total amount and compound interest earned on ₹10,000 invested at 20% interest compounded every 2 years for 8 years?
To find the compound interest and the total amounts after eight year with interest compounded every two years, we'll use the compound interest formula:
Total Amount (A) = P(1 + r/n)¹/²(nt)
Where:
P = Principal = ₹10,000
r = Rate of interest = 20% = 0.2
n = Number of times the interest is compounded in a year (every 2 years, so n = 1/2)
t = Time in years = 8 years
Convert the interest rate to a decimal by dividing by 100:
20% ÷ 100 = 0.2
A = ₹10,000x (1 + 0.2¹/²)(1/2 x 8)
Calculate the expression inside the parentheses:
1 + 0.2/(1/2) = 1.4
Calculate the exponent (1/2x 8):
1/2x 8 = 4
Calculate the total amount:
A = ₹10,000 x (1.4)^4
A = ₹10,000 x3.8416
A = ₹38,416
Step 6: Calculate the compound interest:
Total interest = Total amount - Principal
Total interest = ₹38,416 - ₹10,000
Total interest = ₹28,416
So, after eight years, the total amount is ₹38,416 and the compound interest is ₹28,416.
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It says to determine whether the following symbolized arguments are valid or invalid by constructing the truth table for each?
The valid symbolized arguments is HS-valid. (option e).
Now let's focus on the symbolized arguments presented in this question. To determine their validity, we need to identify the form of each argument. In some cases, we may need to rewrite the argument using double negation or commutativity before assigning a name to its form.
The argument form known as Hypothetical Syllogism (HS) is represented as follows:
P⊃Q
Q⊃R
P⊃R
The given argument can be rewritten using double negation as follows:
H⊃~M
M⊃H
H⊃~H
Then, we can see that the argument follows the form of HS, where if H implies not M, and not M implies not H, then we can conclude that H implies not H. This conclusion is always true because it is a contradiction. Therefore, the argument is valid.
Hence the correct option is (e).
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Complete Question:
Determine whether the following symbolized arguments are valid of invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named for. Those arguments without a specific name are valid.
H⊃~M
M
______
~H
a. DA-Invalid.
b. MP-valid.
c. AC-invalid.
d. MT-valid.
e. HS-valid.
Prove that sum of measure of three angles of triangle is 180
Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem
To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:
Sum of measures of interior angles of triangle = (n-2) × 180 degrees
= (3-2) × 180 degrees [since we are dealing with a triangle]
= 1 × 180 degrees
= 180 degrees
Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.
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B=6,c=7.5 what is A in Pythagorean therom
Answer: 4.5
Step-by-step explanation:
A^2 +B^2 =C^2
A^2 + 6^2 =7.5^2
A^2 + 36= 56.25
A^2= 20.25
A= square root of 20.25
A= 4.5
use the newton-raphson method to find an approximate value of 3√7 . use the method until successive approximations obtained by calculator are identical. an appropriate function to use for the approximation would be f (x) = A x^2 + B x^3 + C x + D where A= B= C= D=
If c1 = 2, then c2 = ___
2√3= ____
In tests of significance about an unknown parameter of some population, which of the following is considered strong evidence against the null hypothesis?
A. The value of an estimate of the unknown parameter based on a simple random sample from the population is not equal to zero.
B. The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very consistent with the null hypothesis
D. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true.
In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).
We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.
The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.
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PLEASE HELP I DONT HAVE TIME
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
The number of toy soldiers Leo has is 48.
How to calculate the number of toy soldiers Leo has?To solve this problem, we need to find a number that satisfies the three given conditions:
The number is between 27 and 54.
When the number is divided by 4, there is no remainder.
When the number is divided by 7, the remainder is 6.
When the number is divided by 5, the remainder is 3.
Let's start by finding a number that satisfies the first two conditions. We can do this by listing the multiples of 4 between 27 and 54:
28, 32, 36, 40, 44, 48, 52
Next, we need to find which of these numbers also satisfies the third condition, that is, leaves a remainder of 6 when divided by 7. We can go through each of these numbers and check:
28 divided by 7 leaves a remainder of 0.
32 divided by 7 leaves a remainder of 4.
36 divided by 7 leaves a remainder of 1.
40 divided by 7 leaves a remainder of 5.
44 divided by 7 leaves a remainder of 2.
48 divided by 7 leaves a remainder of 6.
52 divided by 7 leaves a remainder of 3.
So, the only number that satisfies the first three conditions is 48.
Finally, we need to check if 48 also satisfies the fourth condition, that is, leaves a remainder of 3 when divided by 5. Indeed, 48 divided by 5 leaves a remainder of 3.
Therefore, the number of toy soldiers Leo has is 48.
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Professor Krugman's economics course, the correlation between the students' total scores prior to the final examination and their final‑examination scores is r=0.5.r=0.5. The pre‑exam totals for all students in the course have mean 280280 and standard deviation 40.40. The final‑exam scores have mean 75 and standard deviation 8.. Professor Krugman has lost Julie's final exam but knows that her total before the exam was 300.300. He decides to predict her final‑exam score from her pre‑exam total.What is the slope of the least-squares regression line of final-exam scores on pre-exam total scores in this course? Give your answer to one decimal place.
Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.
What is Standard Deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.
(a) Slope, b = r*(sy/sx) = 0.5*(8/40) = 0.1
Intercept = y - bx = 75 - 0.1*280 = 47
The regression equation is:
y = 47 + 0.1*x
(b) Put x = 300
y = 47 + 0.1*300
y = 77
(c) r2 = 0.5*0.5 = 0.25
Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.
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2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if
a) A answers the first question,
b) B answers the first question.
a) The probability that A wins if A answers the first question is α / (α + β).
b) The probability that A wins if B answers the first question is βα+β.
a) If A answers the first question, then the game will be over only if A answers the first question correctly, which has a probability of α. If A answers incorrectly, then B gets to answer the next question, and we are in the same situation but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:
P(A wins | A answers first) = α + (1 - α)β P(A wins | B answers first)
b) If B answers the first question, then we are in the same situation as in part a) but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:
P(A wins | B answers first) = β P(A wins | A answers first) + (1 - β)β P(A wins | B answers first)
We can solve these equations for P(A wins | A answers first) and P(A wins | B answers first) using algebraic manipulation. For example, we can rearrange the equation in part a) to get:
P(A wins | A answers first) = α / (1 - (1 - α)β)
Similarly, we can rearrange the equation in part b) to get:
P(A wins | B answers first) = β / (1 - (1 - β)α)
Note that these probabilities depend on the values of α and β, which represent the abilities of A and B to answer questions correctly.
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the graph of the sales of a new product at a candy store, where x is time in months and y is number sold in hundreds, goes through the points (4, 2) and (6, 8). what is the rate of change, in candies sold per month?
The rate of change in candies sold per month is 3 hundred candies.
What is the Rate of change?The momentum of a variable is conveyed by the rate of change, which is used for expressing the percentage change in value over a particular amount of time.
To find the rate of change in candies sold per month, it is necessary to find the slope of the line connecting the two points.
The slope formula is given by: Δ[tex]\frac{y}{x}[/tex][tex]\frac{y2-y1}{x2-x1}[/tex]
Using the coordinates of the points, [tex]\frac{8-2}{6-4} =\frac{6}{2} =3[/tex]
The slope is 3. This means that for every month, the store sells 300 more candies.
Therefore, the rate of change, in candies sold per month is 300.
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Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m
Answer:
the cross is the blue color
Complete the sequence in the grids so that starting
of a 2x2 board turned off by pressing one at a time on each
grid we reach all the lit squares.
Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.
What is sequence?In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.
Here,
One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.
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Jose and his children went into a grocery store where they sell apples for $2.25 each and mangos for $1.25 each. Jose has $20 to spend and must buy at least 9 apples and mangos altogether. Also, he must buy at least 3 apples and at most 9 mangos. If � x represents the number of apples purchased and � y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer: $15.25
Step-by-step explanation:
Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:
2.25x + 1.25y ≤ 20 (Jose has $20 to spend)
x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)
x ≥ 3 (Jose must buy at least 3 apples)
y ≤ 9 (Jose can buy at most 9 mangos)
To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.
First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:
When x = 0, we have 1.25y = 20, so y = 16.
When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).
Plotting these intercepts and connecting them with a line, we get:
| *
16 | *
|
| /
| /
|/
0 *--------*
0 8.89
Next, we graph the line x + y = 9 by finding its intercepts:
When x = 0, we have y = 9.
When y = 0, we have x = 9.
Plotting these intercepts and connecting them with a line, we get:
|
9 | *
|
| /
| /
|/
0 *--------*
0 9
Finally, we shade the feasible region by considering the remaining constraints:
x ≥ 3: This means we shade to the right of the line x = 3.
y ≤ 9: This means we shade below the line y = 9.
Shading these regions and finding their intersection, we get:
| *
16 | * |
| |
| / |
| / |
|/ |
9 *--------*---
| | /
| |/
| *
0 *--------*
3 8.89
The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.
To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.
The mean height of 15 pupils is 159 cm. One of these pupils is 148 cm and leaves the group. Determine the new mean height of the group. Give your answer correct to 1 decimal place.
Using the mean formula we know that the new mean height of 14 people is 159.7 cm.
What is mean?A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.
For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
The mean height given is 159 cm.
Let, x1, x2, x3 ..... x15 be the height of 15 people.
x1+x2+x3 ..... x15/15 = 159
x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)
Let, x1 = 148 cm, who leaves the group.
148+x2+x3 ..... x15 = 2385 cm
x2+x3 ..... x15 = 2237 cm
Now, we have 14 people.
New mean = x2+x3 ..... x15/14
= 2237/14
= 159.7 cm
Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.
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y=2x+1
2x-y=3
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Can someone help me with this
Solving a system of equations we can see that he cost of a corn dog is $1.25 and the cost of the fries is $3.50
How to find the cost of each item?We can define two variables here:
x = cost of a corn dog.
y = cost of the fries.
With the information in the question we can write two equations, these two equations form a system of equations that we can solve, the system of equations is the one below:
2x + 3y = 13
4x + y = 8.50
We can isolate y in the second equation to get:
y = 8.50 - 4x
Replace it in the other one:
2x + 3*(8.5 - 4x) = 13
2x + 25.5 - 12x = 13
-10x = 13 - 25.5
x = -12.5/-10 = 1.25
Then:
y = 8.5 - 4*1.25 = 3.5
The cost of a corn dog is 1.25 dollars and the cost of the fries is 3.50 dollars.
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If the sum of two numbers is 10 and the product of the numbers is 15, then find the following:
(a) The difference of numbers.
(b) Sum of cube of the numbers.
Answer:
the numbers are
[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]
Step-by-step explanation:
then there difference is
square root of 10 + 5 -(- square root of 10 +5)
=
[tex]2 \sqrt{10} [/tex]
and the cube of there sum is 15^3 = 15* 15* 15
= 3375
please help
there are 2 possible answers
Let x be the number of boys in a class and y be the number of girls. Which equation represents 2 boys for
every 5 girls? Select all that apply.
A. x=2y-5
B. x=5y-2
C. 5x=2y
D. x=2 1/2y
E. x=2/5y
Answer:
C, E
Step-by-step explanation:
You want the equations that represent 2 boys for every 5 girls in a class.
RatioThe number of boys is represented by x, and the number of girls is represented by y, so you have ...
x : y = 2 : 5
As fractions, this is ...
x/y = 2/5
Other representationsMultiplying by 5y gives ...
5x = 2y . . . . . . matches equation C
Dividing by 5, we have ...
x = 2/5y . . . . . . matches equation E
Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged
The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.
To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.
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The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5
None of the available options match the parabola's equation.
Which might be the parabola's equation?To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.
A parabola's vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the parabola's vertex.
[tex]y = a(x-5)^2 - 3[/tex]
These values are substituted into the equation to produce:
[tex]-15 = a(2-5)^2 - 3[/tex]
[tex]-15 = 9a - 3[/tex]
[tex]-12 = 9a[/tex]
[tex]a = -4/3[/tex]
[tex]y = (-4/3)(x-5)^2 - 3[/tex]
This equation is expanded and simplified to produce:
[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
The perimeter of the figure is 16p + 10.
What is perimeter?The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.
The perimeter of a figure is the sum of the lengths of all its sides.
Thus,
Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)
Perimeter = 2p + 2(7p) + 2(5)
Perimeter = 16p + 10
Hence, the perimeter of the figure is 16p + 10.
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The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week:
On a grid, Label Hours Studying on x axis and Test Scores on y axis. The title of the graph is Test Scores and Hours Studying. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 10 and 2, 25 and 3.1, 10.1 and 4, 30 and 4, 45 and 5, 45 and 6, 25 and 6.5, 60 and 7, 45 and 7.5, 50 and 7.5, 75 and 8, 60 and 8.5, 75 and 9, 60. The ordered pair 1, 100 is circled and labeled as M. All the other points are put in an oval and labeled as N.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M. (5 points)
Part B: Describe the association between students' test scores and the number of hours they study. (5 points)
Part A: The group of points labeled N is called a scatter plot. The point labeled M is an outlier.
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The presence of point M could be due to an error in recording data, or it could be due to an unusual event or circumstance that is not representative of the population.
Part B: This suggests that the more time students put into studying, the better their test scores will be. However, it is important to note that the graph does not necessarily imply that studying for more hours will necessarily lead to higher test scores, as the scatter plot also shows that there are other factors that could affect test scores.
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Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score.
Part B: The scatterplot shows a weak positive association between students' test scores and the number of hours they study.
As the number of hours studying increases, the test scores tend to increase, although there is considerable variability in this relationship. The outlier at 1, 100 indicates that there may be other factors other than study time that influence test scores.
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Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to
The 95% confidence interval for the population mean is equal to (30.4,39.6).
A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.
The 95% confidence interval for the population mean is given by:
x(bar) ± Zα/2 * σ/√n
Where,
x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96
Substituting the values, we get:
CI = 35 ± 1.96 * 100/√25
CI = (30.4,39.6)
Hence, the 95% confidence interval for the population mean is (30.4,39.6).
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Can someone help me find the elevation of the sun I need the answers that are highlighted in yellow please help image below
Answer:
Step-by-step explanation:
a. ∠ACB
b. AC
c. AB
d. BC
e. tangent, opposite, adjacent
f. m∠ACB = tan⁻¹(34/45) = 37°
Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only
The coordinate matrix LFE of L relative to the ordered bases E and F is given by:
LFE=12,3,0,12,3,0,0
LFE =
[[5, 1, 3, 3],
[0, 0, 3, 0],
[0, 0, 0, 0]]
This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:
LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12
LFE[1,2] = L(e2) = = 0 + 0 + 3 + 0 = 3
LFE[1,3] = L(e3) = = 0 + 0 + 0 + 0 = 0
LFE[2,1] = L(f1) = = 5 + 1 + 3 + 3 = 12
LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3
LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0
LFE[3,1] = L(f4) = = 0 + 0 + 0 + 0 = 0
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Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.
The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.
what is volume?
Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
The volume of the rectangular prism without the cylinder can be calculated as:
[tex]$$V_1 = A \times h$$[/tex]
where A is the base area and h is the height
[tex]$$V_1 = 2250 \times 100$$[/tex]
[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]
The volume of the cylinder can be calculated as:
[tex]$$V_2 = \pi r^2 h$$[/tex]
where r is the radius and h is the height
[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]
[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]
The volume of the rectangular prism with the cylinder missing can be calculated as:
[tex]$$V = V_1 - V_2$$[/tex]
[tex]$$V = 225000 - 196349.54$$[/tex]
[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]
Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).
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f² + 7f + 10 = (ƒ +_)(ƒ +_)
Whats this answer i dont get it pls domeone help me <33
Answer:
To factorize the quadratic expression f² + 7f + 10, we need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5. So, we can write:
f² + 7f + 10 = (f + 2)(f + 5)
Therefore, the answer is (f + 2)(f + 5).
Answer:
Step-by-step explanation:
[tex]f^2+7f+10=f^2+2f+5f+10=f(f+2)+5(f+2)=(f+5)(f+2)[/tex]
By grouping, we can factor the polynomial. We know that 2+5=7 and 2*5=10, so this is why (f+5) and (f+2) are factors of f²+7f+10.
