The answers for the questions given are mentioned below respectively.
Define the term expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.
It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.
8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.
8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.
8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .
8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.
8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.
8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.
8.17 - The correct truth value of the statement is: c. Some A are B. (T)
8.18 - The correct truth value of the statement is: e. Some A are B. (T)
8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)
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The following set of scores was obtained from a quiz: 4, 5, 8,9, 11, 13, 15, 18, 18, 18, 20. The teacher computes the usual descriptive measures of central tendency and spread for these data and then discovers that an error was made. One of the 18s should have been a 16. Which of the following measures will NOT need to be changed from the original computations? (There may be more than one correct answer.) Mean 73 Median Standard deviation 1 IQR They all will need to be changed.
All of the measures of central tendency and spread for these data will need to be changed from the original computations in order to reflect the correct values.
In this case, the initial set of scores was 4, 5, 8, 9, 11, 13, 15, 18, 18, 18, and 20. The teacher initially computed the mean, median, standard deviation, and IQR and then discovered that one of the 18s should have been a 16.The mean is affected by any change in the data, so this measure will need to be changed to reflect the correct values. The new mean is 73.The median is also affected by any change in the data, so this measure must be recalculated to reflect the correct values.
The new median is 15.5.The standard deviation measures the spread of data from the mean, so this measure must also be changed to reflect the correct values. The new standard deviation is 1.4.Finally, the IQR measures the spread of the middle 50% of the data, so this measure must also be changed to reflect the correct values. The new IQR is 6. All of the measures of central tendency will need to be changed.
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The sales of books at a local book fair are shown in the histogram.
A histogram titled Book Sales with the x-axis labeled Number of Books. The x-axis has intervals of 0 to 1, 2 to 3, 4 to 5, 6 to 7, 8 to 9 and 10 to 11. The y-axis is labeled Frequency and starts at 0 with tick marks every two units up to 10. There is a shaded bar above 1 to 3 that stops at 3, above 2 to 3 that stops at 4, above 5 to 6 that stops at 8, above 6 to 7 that stops at 2, above 8 to 9 that stops at 4 and above 10 to 11 that stops at 8.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 11. This might be because the book fair offers fair prices, so most costumers bought books.
The data is skewed, with a maximum range of 14. This might be because many of the customers wanted to stock up before the winter.
The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
The data is symmetric with a maximum range of 10. This might mean that most customers bought less than 3 books because that is all that they could carry.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter."
What is a histogram?A histogram is a type of graph used in statistics to represent the distribution of a set of continuous data. It consists of a set of adjacent bars, where the area of each bar represents the frequency or relative frequency of observations within a specific interval or "bin" of the data.
The x-axis of a histogram shows the range of values for the variable being measured, divided into intervals or bins. The y-axis shows the frequency or relative frequency of observations within each interval or bin. Histograms are commonly used to show the shape, center, and spread of a distribution of data, as well as any potential outliers or gaps in the data.
In the given question, the histogram shows a skewed distribution, where the majority of book sales occurred in the lower intervals (1-3, 2-3, and 5-6) and the frequency decreases as the number of books sold increases. The maximum range of the data is 14 (from the interval 10-11 to the interval 2-3), which suggests a wide spread of book sales across different intervals.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter." comes the closest to describing the spread and distribution of the data shown in the histogram.
The other options do not accurately describe the shape or spread of the data shown in the histogram.
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Answer:
C: The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
Step-by-step explanation:
After how many weeks do you think it would be unreasonable to continue counting individual mosquitoes? And finally, at the end of the 13-week mosquito season, how many mosquitoes would you expect to be in the trap? Use complete sentences to explain both of your answers below.
At the end of the 13-week mosquito season, we would expect to find around 558 mosquitoes in the trap.
It would be unreasonable to continue counting individual mosquitoes after about 13 weeks, since that is usually the end of the mosquito season. This is because, after the 13th week, the number of mosquitoes captured in the trap is likely to decrease significantly, making it pointless to count them individually. At the end of the 13-week mosquito season, the expected number of mosquitoes in the trap can be estimated using a simple exponential decay function.
Assuming the initial number of mosquitoes in the trap is N0 and the rate of decay is k, the number of mosquitoes after t weeks (Nt) can be calculated using the following equation: [tex]Nt = N0 * e-kt.[/tex]
For example, if the initial number of mosquitoes in the trap is 1000 and the rate of decay is 0.2, then the number of mosquitoes after 13 weeks can be estimated as follows:[tex]N13 = 1000 * e-0.2*13 = 558[/tex]
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Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
Can someone help me with this
Answer:
they bought 62 item from noodles and 51 items from hot chips
Can someone help me with this math problem pls! #Percents
Answer: $3.64
Step-by-step explanation:
At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.
Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.
Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.
Let f(x)=x2−4. What is the average rate of change of f(x) from −5 to −2 ?
A. -1/7
B. 1/7
C. -7
D. 7
Answer:
Step-by-step explanation:
To find the average rate of change of the function f(x) from -5 to -2, we need to calculate:
(f(-2) - f(-5))/(-2 - (-5))
First, let's find f(-2) and f(-5):
f(-2) = (-2)^2 - 4 = 0
f(-5) = (-5)^2 - 4 = 21
Substituting these values in the above formula, we get:
(0 - 21)/(-2 + 5) = -21/3 = -7
Therefore, the average rate of change of f(x) from -5 to -2 is -7.
So the answer is (C) -7.
A 40-year-old person who wants to retire at age 60 starts a yearty retirement contribution in the amount of $6,000. The retirement account is forecasted to average a 5% annual
rate of retum, ylelding a total balance of $198,395.72 at retirement age.
If this person had started with the same yearty contribution at age 30, what would the difference be in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
O $200,732.63
O $200,237.36
O $398,633.09
O S389.633.90
Para calcular la diferencia en los saldos de la cuenta de jubilación, necesitamos calcular los saldos en ambos casos y luego restarlos.
Para el primer caso, donde la persona comienza a hacer contribuciones anuales a los 40 años, tenemos:
Número de años hasta la jubilación: 60 - 40 = 20 años
Contribución anual: $6,000
Tasa de interés anual: 5%
Usando la fórmula para el valor futuro de una serie de pagos (anualidades) ordinarias, tenemos:
VF = Pmt x [(1 + r)^n - 1] / r
Donde VF es el valor futuro (saldo de la cuenta), Pmt es la contribución anual, r es la tasa de interés anual y n es el número de períodos (en este caso, el número de años hasta la jubilación).
Entonces, para este caso, el saldo de la cuenta sería:
VF = $6,000 x [(1 + 0.05)^20 - 1] / 0.05 = $198,395.72
Para el segundo caso, donde la persona comienza a hacer contribuciones anuales a los 30 años, tenemos:
Número de años hasta la jubilación: 60 - 30 = 30 años
Contribución anual: $6,000
Tasa de interés anual: 5%
Usando la misma fórmula que antes, el saldo de la cuenta sería:
VF = $6,000 x [(1 + 0.05)^30 - 1] / 0.05 = $398,633.09
Entonces, la diferencia en los saldos de la cuenta sería:
$398,633.09 - $198,395.72 = $200,237.37
Por lo tanto, la respuesta es la opción B) $200,237.36.
Answer: B- $200,237.36
Step-by-step explanation: Got it right on the test! And also the person above helped me out a lot!!
When comparing the z-scores of values from different data sets, how do I know which one is "better"?
Higher z-scores imply more severe or unusual observations in the data set since they are indicative of values that are further from the mean en terms of standard deviations.
Why do people utilize z-score?With the use of Z-scores, you are able to scale up data points from populations with various means and standard deviations. The comparison of observations for various sorts of variables, which would otherwise be challenging, is now possible thanks to the use of a common scale.
In plain terms, what is z-score?The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from of the mean serve as the unit of measurement for Z-score. The score for a data point is equal to a mean score if the Z-score is 0.
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What is the area of a triangle with a base of 5x - 4 and a height of 2x +6?
The area of the triangle is 5x² + 11x -12 whose base is 5x - 4 and height is 2x + 6.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
According to question:The formula for calculating a triangle's area is:
Area = 1/2 x Base x Height
Plugging in the given values, we get:
Area = 1/2 x (5x - 4) x (2x + 6)
Simplifying, we get:
Area = 1/2 x (10x² + 22x - 24)
Distributing the 1/2, we get:
Area = 5x² + 11x - 12
Therefore, the area of the triangle is 5x² + 11x - 12.
The three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
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a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water. find a) the rotational speed at which the water just touches the bottom of the cylinder and b) the resulting pressure at points a and b.
a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.
a) Rotational speed at which the water just touches the bottom of the cylinder:
We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.
The formula for centripetal force for a liquid with the volume of a cylinder is as follows:
F = (ρr²πh)ω²WhereF:
Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,
we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F
= 377 Nω
= √(F/m)ω
= √(377 N/ 10 kg)ω
= √37.7ω = 6.14 rad/sb)
Pressure at points A and B:
We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:
P = ρgh
Where,
P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP
= 980 Pa
Substituting the given values for point B,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP
= 2156 Pa
The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.
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Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
Given the right triangle below, what is the measure of angle E
The angle E is 50.21°
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
Given, the right angle triangle at ∠F = 90°
According to the figure, base = 16cm, hypotenuse = 25cm
Apply Cosine rule;
Cos x = 16/25
x = Cos⁻¹ (16/25)
x = 50.21°
Therefore, the angle E is 50.21°
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Triangle: According to the question the measure of angle E is 50.21°
What is a triangle?A triangle is a three-sided polygon which has three angles and three vertices. It is one of the basic shapes in geometry and is a fundamental shape in many mathematical and engineering fields. A triangle can be classified according to its angles or sides. Right triangles have one angle that is a right angle (90°) and two acute angles, obtuse triangles have one obtuse angle (greater than 90°) and two acute angles, and equilateral triangles have three equal angles and three equal sides.
Given, the right angle triangle at ∠F = 90°
According to the figure, base = 16cm, hypotenuse = 25cm
Apply Cosine rule;
Cos x = 16/25
x = Cos⁻¹ (16/25)
x = 50.21°
Therefore, the angle E is 50.21°
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What is one possibility for the price of Carlotta’s charges per person
$50 is one estimate for the cost of Carlotta's fees per individual. This is based on information from the article, which claims that some consumers pay $50 a session for Carlotta's services,
which are less expensive than conventional therapy. The precise price, however, is not stated and may change based on the client's financial status and the services rendered. Carlotta's services are priced in the article, although the details are not totally apparent. It states that Carlotta charges less than conventional therapy, indicating that her costs are reasonable and competitive. The article also mentions that some clients pay $50 for each session, which gives a particular pricing range. However, it is crucial to remember that the precise cost may change .
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can you guys help me with this
Answer:
b all real numbers are greater then or equal-2
Solve for x,
using the tangent lines.
X
42°
x = [?]
can someone pls help explain how they got the answer? i’m having a hard time understanding, ty :)
Answer:
138°
Step-by-step explanation:
You want the measure of the angle at two tangents when they intercept an arc of 42°.
Supplementary anglesThe short answer is that the exterior angle x is the supplement of the measure of the arc:
x = 180° -42°
x = 138°
Exterior angleAn exterior angle where secants meet is half the difference of the arcs of the circle they intercept. Here, the secants have been located so the corresponding chord length between the near and far circle intercept points have degenerated to zero. That is, they are tangents.
The angle relation still holds:
x = (long arc - short arc)/2 = ((360° -42°) -42°)/2 = (360° -2·42°)/2
x = 180° -42° = 138°
QuadrilateralThe tangents, together with their associated radii form a quadrilateral. The angles at the tangents are 90°, and the total of all angles is 360°. This gives us the relation ...
x + 90° +42° +90° = 360°
x +42° = 180° . . . . . . . . . . . . . subtract 180°
x = 180° -42° = 138°
(We solved this with an extra step, so you could see the same "supplementary angles" relationship between x and 42°.)
Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. the actual deck will have dimensions 20 feet by 12 feet. what is the scale?
The scale factor of the blueprint of the deck is 1.5 inches = 4 feet
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, Scott has a blueprint of the new deck he is building with dimensions 7.5 inches by 4.5 inches. The actual deck will have dimensions 20 feet by 12 feet.
We need to find the scale factor,
7.5 / 20 = 1.5 / 4
Therefore,
There are 1.5 inches in 4 feet
Hence, the scale factor of the blueprint of the deck is 1.5 inches = 4 feet
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Answer:
hi
Step-by-step explanation:
guvuvugjdhddiebeidgddb
What is the largest number less than 570 that is divisible by 9?
(I need it for a assignment on Beast Academy)
Answer:
567 is the correct number.
Step-by-step explanation:
[tex]5 + 6 + 7 = 18[/tex]
[tex]1 + 8 = 9[/tex]
So 567 is divisible by 9 since
[tex]567 \div 9 = 63[/tex]
Select the correct answer. Which graph represents this equation? A. The graph shows an upward parabola with vertex (minus 3, minus 4.5) and passes through (minus 7, 3.5), (minus 6, 0), (0, 0), and (1, 3.5) B. The graph shows an upward parabola with vertex (3, minus 4.5) and passes through (minus 1, 3.5), (0, 0), (6, 0), and (7, 3.5) C. The graph shows an upward parabola with vertex (minus 2, minus 6) and passes through (minus 5, 7), (minus 4, 0), (0, 0), and (1, 7) D. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7)
Answer:
A
Step-by-step explanation:
Use the given information below to answer the questions. Show ALL your work.The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches.LetM = the height of a randomly selected young manW = the height of a randomly selected young woman1. Describe the shape, center, and spread of the distribution of M-W.2. Find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman.
We have that, The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is 0.709
How do we find the probability?1. The shape, center, and spread of the M-W distribution are:Shape: NormalCenter: 4.8 inches (69.3 - 64.5)Spread: The standard deviation of the difference between two normally distributed variables is given by the formula:
[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]
Let us define [tex]Z = (M - W - 2)/3.64[/tex]. So the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is:
[tex]P(M > W + 2) = P((M - W - 2)/\sigma(M-W) > (- 2)/\sigma (M-W)) = P(Z > -0.55) = 1 - P(Z \leq - 0.55)[/tex]
Using a standard normal table or a calculator, we find that [tex]P(Z \leq -0.55) \approx 0.291[/tex]. Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx 1 - 0.291 = 0.709[/tex].
The shape, center, and spread of the M-W distribution are:
Shape: Regular Center: 4.8 inches (69.3 - 64.5)
Dispersion: The standard deviation of the difference between two normally distributed variables is given by the formula:
[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]
The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx 0.709[/tex].
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What’s is the answer to this
Answer:
What is the measure of angle F?
B. 65Step-by-step explanation:
You're welcome.
the answer i need is Another pair it could be (_,10)
and every y value is _ every x value
Answer:
Another order pair could be (30,10).
Every y value is "one-third of" every x value.
Use the factorization A PDP 1 to compute Ak, where k represents an arbitrary integer. a 7(b-a) 17 a 017
If A = [tex]PDP^{-1}[/tex], Then [tex]A^{k}[/tex] = [tex](PDP^{-1}) ^{k}[/tex] = [tex]PDP^{-1}[/tex][tex]PDP^{-1}[/tex] .....[tex]PDP^{-1}[/tex] = [tex]PD^{k} P^{-1}[/tex]since [tex]P^{-1}[/tex] P = I, the identity matrix.
Further, the representation can be made as in the following attachment.
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if there is a sample, the standard error is used in the denominator of the z stat or t stat formula. group of answer choices true false
It is correct to state that if there is a sample, the standard error is used in the denominator of the z stat or t stat formula.
What is the formula for the test statistic?The t-distribution is used when we have the standard deviation for the sample instead of the population, hence the equation is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The standard error is modeled as follows:
[tex]s_e = \frac{s}{\sqrt{n}}[/tex]
Which is the denominator of the formula for the test statistic, hence the statement is true.
When we have the standard deviation for the population, we use the z-distribution, however the formula for the standard error is similar.
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y=-x+2
please anwser quickly as you can
Answer: -2.0
Step-by-step explanation:
a researcher compares the effectiveness of two different instructional methods for teaching anatomy. a sample of 116 students using method 1 produces a testing average of 50.3. a sample of 151 students using method 2 produces a testing average of 68.6. assume that the population standard deviation for method 1 is 15.62, while the population standard deviation for method 2 is 17.21. determine the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2. step 3 of 3 : construct the 99% confidence interval. round your answers to one decimal place.
The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is [15.8, 20.8].
The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 can be calculated using a two-sample t-test.
First, calculate the sample difference in means. Subtract the mean for method 1 (50.3) from the mean for method 2 (68.6) to get 18.3.
Next, calculate the pooled standard deviation, which is the weighted average of the standard deviations for each sample:
Pooled standard deviation = [tex]√(((n1-1)×s12 + (n2-1)×s22)/ (n1+n2-2))[/tex]
n1=116, s12=15.62, n2=151, s22=17.21
Pooled standard deviation = [tex]√(((116-1)×15.62 + (151-1)×17.21)/ (116+151-2))[/tex]
Pooled standard deviation = [tex]√(1422.3788/265)[/tex]
Pooled standard deviation = 4.89
Finally, calculate the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2:
99% Confidence Interval = Sample Difference in Means ± (Critical Value) × (Pooled Standard Deviation/√(n1+n2))
99% Confidence Interval =[tex]18.3 ± (2.58) × (4.89/√(116+151))[/tex]
99% Confidence Interval = 18.3 ± 2.50
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A cruise ship compartment can hold 440 pieces of luggage. If a ship had 42 compartments,how many pieces of luggage can it hold?
Answer: 18480
i used a calculator :)
match the following. 1. a length equal to the height in a square 2. any rhombus can be created by rotating this shape around the midpoint of its base 3. found by dividing 360 by the number of sides of a regular polygon 4. height of a parallelogram 5. each angle in a rectangle 6. a special type of trapezoid 7. perpendicular distance from the center of a regular polygon to its side 8. a special type of regular polygon
Altitude
base
apothem
parallelogram
isosceles triangle
right angle central angle
The following points are matched:
A length equal to the height in a square - baseAny rhombus can be created by rotating this shape around the midpoint of its base - right angle (square)Found by dividing 360 by the number of sides of a regular polygon - central angleHeight of a parallelogram - altitudeEach angle in a rectangle - right angleA special type of trapezoid - parallelogramThe perpendicular distance from the center of a regular polygon to its side - apothemA special type of regular polygon - equilateral triangleAll sides of a square are equal.On rotating a square around the midpoint of its base, a rhombus is created. This happens due to the right angles between the sides of the square.The central angle of a regular polygon is obtained by dividing 360 by the number of sides of the same polygon.The altitude of a parallelogram is defined as its height.By the property of a rectangle, it has only right angles.A trapezoid is a quadrilateral with at least one pair of parallel sides while a parallelogram has both pairs of parallel sides.The apothem is the perpendicular distance from the center of a regular polygon to its side.An equilateral triangle is a special type of regular polygon with three equal sides and three equal angles.Thus, the definitions are matched to their respective terms.
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there are 30 aaa batteries in a box and 9 are defective. two batteries are selected without replacement. what is the probability of selecting a defective battery followed by another defective battery
Therefore, the probability of selecting a defective battery followed by another defective battery is about 12/145 or 8.28%.
What is the probability?The probability of selecting a defective battery on the first draw is 9/30, or 3/10, since there are 3 defective batteries out of 30 total.
Since one battery has already been drawn, there are now 29 batteries left in the box, and 8 defective batteries remaining. The probability of selecting another defective battery on the second draw, without replacement, is 8/29.
To find the probability of both events happening (selecting a defective battery followed by another defective battery), we multiply the probabilities of each event:
P(defective battery and then another defective battery) = P(defective battery on first draw) × P(defective battery on second draw)
P(defective battery and then another defective battery) = (3/10) × (8/29)
P(defective battery and then another defective battery) = 24/290 = 0.0828 or 8.28%
Therefore, the probability of selecting a defective battery followed by another defective battery out of 30 AAA batteries in a box where 9 are defective and two batteries are selected without replacement is 0.0828 or 8.28%.
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help me please........................................................
Answer:
To find the area of the given figure, we can divide it into two separate shapes, a rectangle and a triangle, and then add their areas together.
First, we can find the area of the rectangle by multiplying its length and width. From the diagram, we can see that the length of the rectangle is 12 cm and the width is 5 cm.
Area of rectangle = length x width
Area of rectangle = 12 cm x 5 cm
Area of rectangle = 60 cm^2
Next, we can find the area of the triangle by using the formula for the area of a triangle, which is:
Area of triangle = 1/2 x base x height
From the diagram, we can see that the base of the triangle is 5 cm and the height is 8 cm.
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 5 cm x 8 cm
Area of triangle = 20 cm^2
Finally, we can find the total area of the figure by adding the area of the rectangle and the area of the triangle:
Total area = area of rectangle + area of triangle
Total area = 60 cm^2 + 20 cm^2
Total area = 80 cm^2
Therefore, the area of the given figure is 80 square centimeters.
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