The assumptions necessary for confidence interval 90% with population mean salary μ turns out to be (1000, 2100) this interval is based on sample size 25 is given by option C) The population must have an approximately normal distribution.
For a confidence interval to be valid, it is necessary to make certain assumptions about the population and the sample.
Here, the assumptions necessary for a valid 90% confidence interval based on a sample of size n = 25 are,
Random sampling,
The sample should be a random sample from the population.
That every member of the population has an equal chance of being selected.
Independence,
The sample observations should be independent of each other.
The value of one observation does not affect the value of another observation.
Normality,
The population of salaries must have an approximately normal distribution.
This assumption is necessary because the confidence interval is based on the Central Limit Theorem.
Which states that the sampling distribution of the sample mean is approximately normal.
Provided that the sample size is large enough and the population distribution is approximately normal.
Sample size,
The sample size should be large enough to ensure that the sampling distribution of the sample mean is approximately normal.
In general, a sample size of 25 is considered sufficient to meet this requirement.
Option A is incorrect because it describes an assumption necessary for the validity of a confidence interval based on the Central Limit Theorem.
Option B is incorrect because the population is assumed to have a normal distribution, not an approximate t-distribution.
Option D is incorrect because it describes a biased sample distribution.
Which would invalidate the results of any statistical analysis based on the sample.
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levene's test is violated for use of a student's t-test. what is the best decision to make in order to analyze these data? choose the best answer. group of answer choices ignore levene's test; the larger group has the larger variance. ignore levene's; the groups sizes are equal use welch's t-test because levene's is violated.
Levene's test is not recommended. It is also important to ensure that the group sizes are equal for accurate results.
If Levene's test is violated for use of a student's t-test, the best decision would be to use Welch's t-test because it can handle unequal variances between the groups.
Levene’s test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. Some common statistical procedures, such as analysis of variance and t-tests, assume that variances of the populations from which different samples are drawn are equal. Levene’s test assesses this assumption
It is important to take into consideration that the larger group may have a larger variance, which can affect the results. Therefore, ignoring Levene's test is not recommended. It is also important to ensure that the group sizes are equal for accurate results.
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a boat leaves the marina and sails 3 miles north, then 2 miles northeast. how far from the marina is the boat, and in what direction must it sail to head directly back to the marina?
The boat is approximately 4.12 miles from the marina and its direction is northeast. To head directly back to the marina, the boat must sail southwest.
To determine the boat's distance from the marina and the direction to head back, we'll use the Pythagorean theorem and some trigonometry.
After sailing 3 miles north and 2 miles northeast, the boat's total displacement is a right-angled triangle with legs of 3 miles (north) and 2√2 miles (east). The hypotenuse represents the straight-line distance back to the marina.
Using the Pythagorean theorem, distance^2 = (3^2) + (2√2)^2 = 9 + 8 = 17. So, the distance is √17 ≈ 4.12 miles.
To find the direction, we'll calculate the angle formed by the northward displacement and the straight-line path back to the marina. Using tangent, tan(angle) = (2√2)/3. The angle is arctan(2√2/3) ≈ 49.1 degrees.
So, the boat is approximately 4.12 miles from the marina and must sail 49.1 degrees west of south to head directly back to the marina.
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What is the recursive definition for a set of positive integers that are not divisible by 3?
The recursive definition for a set of positive integers that are not divisible by 3 can be defined using two components: a base case and a recursive step.
Two components used for recursive definitionThe base case specifies the starting point, while the recursive step defines the pattern of the sequence.
Base case: The first positive integer not divisible by 3 is 1.
Therefore, the base case is S(1) = 1.
Recursive step:
To generate subsequent integers in the sequence, we can use a rule that adds a fixed constant to the previous integer, provided the result is not divisible by 3. One way to achieve this is by adding 2.
Hence, the recursive step is defined as S(n) = S(n-1) + 2 if (S(n-1) + 2) % 3 ≠ 0, where n > 1 and "%" denotes the modulo operator.
This definition ensures that the sequence consists of positive integers that are not divisible by 3, starting with the base case and following the recursive step.
For example, the first few terms of the sequence would be 1, 4, 5, 7, 10, 11, 13, and so on.
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which bowl holds more water if it is filled to a depth of four units? •the paraboloid z=x2 y2 for 0≤z≤4 •the cone z=x2 y2 for 0≤z≤4 •the hyperboloid z=1 x2 y2 for 1≤z≤5
The Paraboloid z=x2 y2 for 0≤z≤4 holds more water than the hyperboloid z=1 x2 y2 and the cone z = x^2 y^2 when filled to a depth of four units.
To determine which bowl holds more water when filled to a depth of four units, we need to calculate the volume of each shape between z=0 and z=4.
For the paraboloid z=x^2+y^2, we have
V = ∫∫(0≤z≤4) √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA
= ∫∫(0≤z≤4) √(1 + 4x^2 + 4y^2) dA
= ∫(0≤θ≤2π) ∫(0≤r≤2) √(1 + 4r^2) r dr dθ
= π(17^(3/2) - 1)/3
For the cone z = √(x^2 + y^2), we have
V = ∫∫(0≤z≤4) √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA
= ∫∫(0≤z≤4) √(1 + 1/(1+z^2)) dA
= ∫(0≤θ≤2π) ∫(0≤r≤4sinθ) √(1 + 1/(1+(rsinθ)^2)) r dr dθ
= (π/6)(17√17 - 1)
For the hyperboloid z = 1 + x^2 + y^2, we have
V = ∫∫(1≤z≤5) √(1 + (∂x/∂z)^2 + (∂y/∂z)^2) dA
= ∫∫(1≤z≤5) √(1 + 1/(4z^2)) dA
= ∫(0≤θ≤2π) ∫(1≤z≤5) ∫(0≤r≤√((z-1)/(z+1))) √(1 + 1/(4z^2)) r dr dz dθ
= (4/3)(5√5 - 2√2 - 2)
Thus, comparing the volumes, we have
Paraboloid: V = π(17^(3/2) - 1)/3 ≈ 122.92
Cone: V = (π/6)(17√17 - 1) ≈ 121.36
Hyperboloid: V = (4/3)(5√5 - 2√2 - 2) ≈ 59.72
Therefore, the paraboloid holds the most water when filled to a depth of four units.
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what is the value of 6 (-5+3) ÷ 2
Answer:
-2
Step-by-step explanation:
-6 - (-5 + 3) / 2
(-6 — -2) /2
-4/2 = -2
Starting My Account
Imagine that you are at a bank, ready to open your first bank account.
Which actions should you have already taken? Check all that apply.
decided what kind of account I want
Obrought along my Social Security card
compared the services that different banks offer, and learned what they charge for them
Answer:
All options
Step-by-step explanation:
To open a bank account you first need to know which type of account you will open, for example, correct account or savings account. The Social Security card is also required so that the bank has access to your financial history for analysis. Moreover, it is important to compare the different services offered by banks to reduce costs and open the account in the one that suits you best.
Find the missing length. The triangles in each pair are similar.
Answer:
D
Step-by-step explanation:
If we use a different method and divide the big number by the small ones (ex. 54÷45=1.2, 72÷60=1.2) to end up and find that the big triangle is scaled up by 1.2 then we can divide the bug triangles length by 1.2 to get the answer 50.
write java code to generate five random integer numbers, five random double numbers, and five random integers ranging from 1..6
The Java code to generate five random integer numbers, five random double numbers, and five random integers ranging from 1..6 is:
import java.util.Random;
public class RandomNumbers {
public static void main(String[] args) {
Random rand = new Random();
// Generate five random integer numbers
for(int i=0; i<5; i++){
int randInt = rand.nextInt();
System.out.println("Random integer: " + randInt);
}
// Generate five random double numbers
for(int i=0; i<5; i++){
double randDouble = rand.nextDouble();
System.out.println("Random double: " + randDouble);
}
// Generate five random integers ranging from 1..6
for(int i=0; i<5; i++){
int randIntRange = rand.nextInt(6) + 1;
System.out.println("Random integer range: " + randIntRange);
}
}
}
In this code, we first import the Random class from the java.util package. We then create a new Random object called rand.
To generate five random integer numbers, we use a for loop to call the nextInt() method on rand five times. To generate five random double numbers, we use another for loop to call the nextDouble() method on rand five times.
To generate five random integers ranging from 1..6, we use a third for loop to call the nextInt(6) + 1 method on rand five times. The nextInt(6) method returns a random integer between 0 and 5, and adding 1 to this result gives us a random integer between 1 and 6.
Finally, we print out the generated random numbers using the System.out.println() method.
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Solve for length of segment c
Answer:
[tex]\huge\boxed{\sf c = 8\ cm}[/tex]
Step-by-step explanation:
Statement:According to intersecting chords theorem, if two chords intersect, then the product of the two parts of one chords is equal to the product of others.
Solution:So,
11 × c = 10 × 8.8
11c = 88
Divide both sides by 11c = 88/11
c = 8 cm[tex]\rule[225]{225}{2}[/tex]
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) + 7? The y-intercept of the parent function, f(x), is
.
Answer:the answer is 89 for f(x) = x. g(x) if g(x) = f(x) + 7?
all humans are 2 legged, chirpy is 2 legged, therefore chirpy is a human
The given argument "all humans are 2 legged, chirpy is 2 legged, therefore chirpy is a human" is not valid because there could be other creatures, apart from humans, that are also 2 legged.
This is a logical fallacy where one assumes that if a condition is true, then the consequent must also be true. However, this does not necessarily hold true because there could be multiple reasons for the consequent to be true.
In this case, the argument assumes that because all humans are 2 legged and chirpy is 2 legged, chirpy must be a human. However, this argument overlooks the fact that there could be other creatures, apart from humans, that are also 2 legged.
For instance, birds, kangaroos, and even some primates are 2 legged but are not human. Hence, the argument fails to establish a conclusive relationship between the premises and the conclusion.
To prove that an argument is valid, we must ensure that the conclusion necessarily follows from the premises. In this case, the argument does not meet this criterion. Therefore, it is not valid. It is essential to exercise caution when making assumptions, and we must consider all possible scenarios before making a conclusion.
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Complete question is:
Determine whether the following argument is valid and explain how you know.
All humans are 2 legged, chirpy is 2 legged, therefore chirpy is a human
Mr.McMahon pays $880 for a $1000 bond paying bond interest at 9% compounded semi- annually and redeemable at $1000 in 20 years. If his desired yield was 8% compounded semi-annually, what semi-annual probability of default did he expect?
Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.
How to solve?
To solve this problem, we can use the formula for the present value of a bond:
PV = (C/r) ×[1 - 1/(1+r)²n] + F/(1+r)²n
where PV is the present value of the bond, C is the semi-annual coupon payment, r is the semi-annual yield rate, n is the number of semi-annual periods, and F is the face value or redemption value of the bond.
We know that Mr. McMahon paid $880 for a $1000 bond, so the present value of the bond is PV = $880. The redemption value of the bond is F = $1000, and the yield rate that he desired was r = 8% per year, compounded semi-annually. Therefore, the semi-annual yield rate is:
i = 0.08/2 = 0.04
We can use the formula to solve for the number of semi-annual periods:
PV = (C/i) ×[1 - 1/(1+i)²n] + F/(1+i)²n
$880 = ($45/i) ×[1 - 1/(1+0.04)²(220)] + $1000/(1+0.04)²(220)
Solving for i gives:
i = 0.0517 or approximately 5.17%
This is the semi-annual yield rate that Mr. McMahon actually received on the bond. To find the semi-annual probability of default that he expected, we can use the formula for the expected yield rate of a bond:
yield = (1 - probability of default) ×(yield rate on the bond) + (probability of default) ×(recovery rate)
where the recovery rate is the percentage of the face value that would be recovered in the event of default.
Assuming that the recovery rate is zero (meaning that in the event of default, Mr. McMahon would receive nothing), we can solve for the probability of default:
0.08 = (1 - p) ×0.0517 + p ×0
Solving for p gives:
p = 0.357 or approximately 35.7%
Therefore, Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.
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determine whether the following equation is separable. if so, solve the given initial value problem. y 5/5t 6
The particular solution is y = (5/2)t + 9/(5t+6) and this equation is separable since we can write it as:
dy/dt = 5/(5t+6)
Multiplying both sides by (5t+6) gives:
(5t+6)dy/dt = 5
Integrating both sides with respect to t gives:
∫(5t+6)dy = ∫5 dt
Simplifying the integrals gives:
(5/2)t^2 + 6t + C1 = 5t + C2
where C1 and C2 are constants of integration. Solving for y gives:
y = (5/2)t + (C2 - C1 - 6)/(5t+6)
To find the particular solution that satisfies the initial condition y(0) = 2, we substitute t = 0 and y = 2 into the equation above:
2 = (5/2)*0 + (C2 - C1 - 6)/(5*0+6)
Simplifying gives:
C2 - C1 - 6 = 15
Substituting this value of C2 - C1 into the equation for y gives the particular solution:
y = (5/2)t + 9/(5t+6)
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A certain tennis player makes a successful first serve 66% of the time. Assume that each serve is independent of the others. If she serves 5 times, what's the probability she gets a) all 5serves in? b) exactly 4 serves in? c) at least 3 serves in? d) no more than 4 serves in?a) The probability that she gets all 5 serves in is __________.(Round to three decimal places as needed.).b) The probability she gets exactly 4 serves in is ________.(Round to three decimal places as needed.)c) The probability she gets at least 3 serves in is ____________.(Round to three decimal places as needed.)d) The probability that there are no more than 4 serves in is _____________.(Round to three decimal places as needed.)
a) The probability that she gets all 5 serves in is 0.066 (rounded to three decimal places).
b) The probability she gets exactly 4 serves in is 0.278 (rounded to three decimal places).
c) The probability she gets at least 3 serves in is 0.822 (rounded to three decimal places).
d) The probability that there are no more than 4 serves in is 0.934 (rounded to three decimal places).
a) The probability that she gets all 5 serves in is (0.66)^5 = 0.196. (rounded to three decimal places as needed)
b) The probability she gets exactly 4 serves in is (5 choose 4) * (0.66)^4 * (0.34)^1 = 0.387. (rounded to three decimal places as needed)
c) The probability she gets at least 3 serves in is the sum of the probabilities of getting exactly 3, exactly 4, or all 5 serves in:
(5 choose 3) * (0.66)^3 * (0.34)^2 + (5 choose 4) * (0.66)^4 * (0.34)^1 + (0.66)^5 = 0.751. (rounded to three decimal places as needed)
d) The probability that there are no more than 4 serves in is the sum of the probabilities of getting 0, 1, 2, 3, or 4 serves in:
(0.34)^5 + 5 * (0.66)^1 * (0.34)^4 + (5 choose 2) * (0.66)^2 * (0.34)^3 + (5 choose 3) * (0.66)^3 * (0.34)^2 + (5 choose 4) * (0.66)^4 * (0.34)^1 = 0.921. (rounded to three decimal places as needed)
a) The probability that she gets all 5 serves in is 0.066 (rounded to three decimal places).
b) The probability she gets exactly 4 serves in is 0.278 (rounded to three decimal places).
c) The probability she gets at least 3 serves in is 0.822 (rounded to three decimal places).
d) The probability that there are no more than 4 serves in is 0.934 (rounded to three decimal places).
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In ARST, r = 4. 3 inches, s = 8. 9 inches and t=6. 5 inches. Find the measure of ZR to
the nearest 10th of a degree.
Math
The measure of angle ZR is approximately 52.3 degrees to the nearest tenth of a degree.
In a triangle, the amount of the three inside points is 180 degrees. Utilizing the Law of Cosines, we can find the proportion of point R utilizing the given sides:
cos(R) = ([tex]4.3^2 + 6.5^2 - 8.9^2[/tex])/(2 * 4.3 * 6.5)
cos(R) = - 0.312
R = arc cos(- 0.312)
R = 107.5 degrees (adjusted to the closest tenth)
Accordingly, the proportion of point ZR is basically 180 - (90 + R) = 82.5 degrees (adjusted to the closest tenth).Utilizing the Law of Cosines, we can see that the biggest point in the triangle is at vertex S, which estimates roughly 119.5 degrees.
Point R is inverse the side of length 6.5 inches and point Z is inverse the side of length 4.3 inches. The point ZR is the contrast between 180 degrees and the amount of points Z and R. This computation provides us with a proportion of roughly 82.5 degrees.
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The complete question is:
In ARST, r = 4.3 inches, s = 8.9 inches and t=6.5 inches. Find the measure of ZR to the nearest 10th of a degree.
the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 5 to 3. if there were 2949 no votes, what was the total number of votes?
The total number of votes cast in the city was 7864.
Given that there were 2949 no votes, which corresponds to 3 parts of the ratio.
Assume that the total number of votes as x. According to the given information, the ratio of yes votes to no votes is 5 to 3. This means that for every 5 yes votes, there are 3 no votes.
Set up the equation as given:
3 parts = 2949 votes
1 part = 2949 votes / 3
1 part = 983 votes
Now, since the ratio of yes votes to no votes is 5 to 3, a total of 5 + 3 = 8 parts.
Total number of votes = 8 parts × 983 votes per part
Total number of votes = 7864 votes
Therefore, the total number of votes cast was 7864.
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what is the perimeter of the cafe pls answer fast
The perimeter of the cafe is calculated to be equal to 190 feet.
What is the perimeter of a plane shapeA plane shape is a two dimensional figure and its perimeter is the total distance around its outer boundary. It is the sum of the lengths of all its sides.
By careful observation, the cafe have the following lengths at:
left side = 15 + 7 + 16 = 38ft
right side = 3 + 15 + 28 = 46ft
top side = 40 + 3 + 15 = 58ft
bottom side = 48ft
The perimeter of the cafe = 38ft + 46ft + 58ft + 48ft
The perimeter of the cafe = 190 ft.
Therefore, the perimeter of the cafe is calculated to be equal to 190 feet.
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Find the measure of the inscribed angle of questions 1 and 2
The measure of the inscribed angle in each case as required in the task content are;
1. m<P = 83°.2. m<R = 75° and m<S = 96°.What are the measures of the indicated angles?It follows from the task content that the measure of the indicated angles are to be determined.
On this note, Recall that opposite angles of a cyclic quadrilateral are supplementary. In essence, it follows that the sum of the measures of opposite angles of cyclic quadrilaterals equals 180°.
Therefore;
1. m<P + 97° = 180°.
m<P = 83°.
2. m<R + 105° = 180°
m<R = 75°
and
m<S + 84° = 180°.
m<S = 96°.
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The current I(t) in an LC series circuit is governed by the initial value problem below. Determine the current as a function of time t. l"(t)+ 361(t) g(t), I(O) 1, l'(0) 27, where g(t)= {135 sin 3t, 0 ≤ t ≤ 2π 0, 2π
The given initial value problem represents a second-order linear homogeneous differential equation, where coefficient of derivative is 1 and the coefficient of first derivative is 0. current I(t) in LC series as a function of time t circuit is = [tex](-8/19)cos(19t) + (27/19)sin(19t) for 0 ≤ t ≤ 2π.[/tex]
Thus, the characteristic equation of the differential equation is given by [tex]λ^2 + 361 = 0[/tex]. Solving the characteristic equation, we get two complex roots [tex]λ = ±19i.[/tex]
Therefore, the general solution of the differential equation is given by I(t) = [tex]c1cos(19t) + c2sin(19t)[/tex], where c1 and c2 are constants determined by the initial conditions. Differentiating the general solution with respect to t, we get [tex]I'(t) = -19c1sin(19t) + 19c2cos(19t).[/tex]
Using the initial condition I'(0) = 27, we get 27 = 19c2. Therefore, c2 = 27/19. Now, to determine c1, we need to use the initial condition I(0) = 1 and the given function g(t).
When [tex]0 ≤ t ≤ 2π, g(t) = 135sin(3t)[/tex]. Therefore, we have[tex]I(0) = c1cos(0) + c2sin(0)[/tex] = c1 = 1 - c2 = 1 - 27/19 = -8/19. Thus, the current I(t) in LC series circuit is given by [tex]I(t) = (-8/19)cos(19t) + (27/19)sin(19t) for 0 ≤ t ≤ 2π.[/tex]
When t > 2π, g(t) = 0 and the current will continue to oscillate with the same frequency and amplitude, but with different initial conditions determined by the values of I(2π) and I'(2π).
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What is the component form of the vector that translates the top house figure to the bottom house figure?
(7, -2)
(6, -4)
(5, -1)
(-4, 5)
Answer:
The component form of the vector that translates the top - 1 ... 2. Translate rhombus EFGH 2 units to the left, 4 units down, and plot it.
Step-by-step explanation:
P.S i am emo
calculate the area of the circle =6sin() as an integral in polar coordinates. be careful to choose the correct limits of integration.
The area of the circle r = 6sin(θ) in polar coordinates is 9π square units.
How to calculate the area of circle?To calculate the area of the circle r = 6sin(θ) in polar coordinates, we can integrate the expression for the area of an infinitesimal sector of the circle, which is:
dA = (1/2) [tex]r^2[/tex] dθ
Integrating this expression over the limits of θ from 0 to π, we obtain:
A = ∫₀[tex]^\pi[/tex] (1/2) [tex]r^2[/tex] dθ
Substituting r = 6sin(θ), we get:
A = ∫₀[tex]^\pi[/tex] (1/2) (6sin(θ)[tex])^2[/tex]dθ
Simplifying, we have:
A = 18 ∫₀[tex]^\pi[/tex] [tex]sin^2[/tex] (θ) dθ
Using the identity [tex]sin^2[/tex](θ) = (1/2) - (1/2)cos(2θ), we can rewrite the integral as:
A = 18 ∫₀[tex]^\pi[/tex] [(1/2) - (1/2)cos(2θ)] dθ
Evaluating this integral, we get:
A = 18 [(θ/2) - (1/4)sin(2θ)] from 0 to π
Substituting the limits of integration, we get:
A = 18 [(π/2) - (1/4)sin(2π)] - 18 [(0/2) - (1/4)sin(2(0))]
Simplifying, we have:
A = 18 [(π/2) - 0] - 18 [(0) - 0]
A = 18 (π/2)
Therefore, the area of the circle r = 6sin(θ) in polar coordinates is 9π square units.
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The number of home runs that Mark McGwire hit in the first 13 years of his major league baseball career is listed below. (Source: Major League Handbook) Construct a stem-and-leaf plot for this data. 3 49 32 33 39 22 42 9 9 39 52 58 70 6
The stem-and-leaf plot is a useful way to visualize the distribution of the data and to identify any patterns or outliers. We can write the stems on the left-hand side of the plot and the leaves on the right-hand side. Stem and leaf plot : [tex]2 | 2 23 | 2 3 3 9 94 | 2 95 | 2 86 | 07 | 0[/tex]
To construct a stem-and-leaf plot for the given data, we can use the following steps: Identify the stems and leaves: We can use the tens digit as the stem and the ones digit as the leaf. Order the data: We can list the data in ascending order. Separate the data into stems and leaves:
The first column of the plot shows the stems, which are the tens digits of the data. The second column shows the leaves, which are the ones digits of the data.
For example, the first row of the plot shows that McGwire hit 22 home runs in one year. The second row shows that he hit 32, 33, and 39 home runs in different years, and so on.
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What is the answer please
The expression that can be express in the form (ax + b)(ax - b), are x² - 9 and 9x² - 4.
How to solve quadratic equation?The expression that can be written in the form (ax + b)(ax - b), where a and b are integers can be represented as follows:
Therefore,
The expression should be able to be express in the form as follows:
(ax + b)(ax - b)
x² - 9 = (x - 3)(x + 3)
Therefore,
(x - 3)(x + 3) = x² + 3x - 3x - 9
x² + 3x - 3x - 9 = x² - 9
Therefore,
(x - 3)(x + 3) = x² - 9
9x² - 4 = (3x + 2)(3x - 2)
(3x + 2)(3x - 2) = 9x² - 6x + 6x - 4
9x² - 6x + 6x - 4 = 9x² - 4
Therefore, the expression are x² - 9 and 9x² - 4
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bob makes a 95% confidence interval with a random sample of 100 and his margin of error is plus or minus 18. in order to cut the margin of error in half next time, what should bob's sample size be?
If he wants to maintain the same level of confidence (95%), his new sample size should be 400. This means that his margin of error will be plus or minus 9. It's important to note that the margin of error is affected by both the sample size and the level of confidence.
To cut the margin of error in half, Bob should increase his sample size. The margin of error is related to the sample size by the formula:
Margin of Error = Z * (Standard Deviation / sqrt(Sample Size))
Here, Z represents the Z-score associated with the desired confidence level (95% in this case). To halve the margin of error, the sample size should be increased by a factor of 4. This is because when you divide the margin of error by 2, you need to compensate by multiplying the denominator by 4 to maintain equality.
So, if Bob's current sample size is 100, he should increase it to:
New Sample Size = 100 * 4 = 400
By using a sample size of 400, Bob can cut his margin of error in half while maintaining the same 95% confidence level.
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The probability that a patient recovers from a stomach disease is 0:8. Suppose 20 people are known to have contracted this disease. What is the probability that exactly 14 recover, at least 14 recover, at least 14 but not more than 18 recover, and at most 16 recover?
P(X<=16) = 1 - P(X>16)
= 1 - (P(X=17) + P(X=18) + ... + P(X=20))
= 0.998
This is a binomial distribution problem, where we have a fixed number of trials (20 patients), each trial can have one of two outcomes (recover or not recover), and the Probability of success (recovering) is 0.8. We can use the binomial probability formula to solve each part of the problem:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
P(X=k) is the probability of getting k successes
n is the total number of trials
k is the number of successes we want to find the probability for
p is the probability of success for each trial
(1-p) is the probability of failure for each trial
(n choose k) is the binomial coefficient, which is the number of ways to choose k successes out of n trials.
Using this formula, we can solve each part of the problem:
Probability that exactly 14 recover:
P(X=14) = (20 choose 14) * (0.8)^14 * (0.2)^6
= 0.214
Probability that at least 14 recover:
P(X>=14) = P(X=14) + P(X=15) + P(X=16) + ... + P(X=20)
To calculate this, we can use a binomial cumulative distribution table or calculator, or we can use the complement rule:
P(X>=14) = 1 - P(X<14)
= 1 - (P(X=0) + P(X=1) + ... + P(X=13))
= 1 - ((20 choose 0) * (0.8)^0 * (0.2)^20 + (20 choose 1) * (0.8)^1 * (0.2)^19 + ... + (20 choose 13) * (0.8)^13 * (0.2)^7)
= 0.993
Probability that at least 14 but not more than 18 recover:
P(14<=X<=18) = P(X=14) + P(X=15) + ... + P(X=18)
To calculate this, we can use a binomial cumulative distribution table or calculator, or we can subtract the probabilities of getting fewer than 14 and more than 18:
P(14<=X<=18) = P(X>=14) - P(X>=19)
= 0.993 - (P(X=19) + P(X=20))
= 0.007
Probability that at most 16 recover:
P(X<=16) = P(X=0) + P(X=1) + ... + P(X=16)
To calculate this, we can use a binomial cumulative distribution table or calculator, or we can use the complement rule:
P(X<=16) = 1 - P(X>16)
= 1 - (P(X=17) + P(X=18) + ... + P(X=20))
= 0.998
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Find the value of x and round it up to the nearest tenth
Tan (x) = 5.3/12
The exact value of x is 44.16°. The value of x rounded up to the nearest tenth is 44.2°.
What is inverse of the tangent?The inverse of the tangent function is denoted by the symbol ‘tan⁻¹’. The inverse of the tangent function helps to find the angle of a right triangle when the ratio of the opposite side to the adjacent side is known.
The given equation can be solved using the inverse of the tangent function.
Therefore, we can solve the equation by applying the inverse tangent function:
tan⁻¹ (5.3/12) = x
To calculate the exact value of x, we can use a calculator to find the inverse of the tangent of 5.3/12.
The exact value of x is 44.16°.
However, to round the value of x to the nearest tenth, we need to look at the tenths place. The tenths place for 44.19° is 6.
Therefore, the value of x rounded up to the nearest tenth is 44.2°.
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mona had 6 50 rupees she exchange the whole amount for 50 rupee notes how many 50 rupee notes did she get
Step-by-step explanation:
the answer is = 650/50 = 13
so, she got 13, 50 rupee note.
hope this helps.
4. Lin wants to get some custom T-shirts printed for her basketball team. Shirts cost $10
each if you order 10 or fewer shirts and $9 each if you order 11 or more shirts.
a. Make a graph that shows the total cost of buying shirts, for 0 through 15 shirts.
price
Answer:
Sure, I can help you with that. To make a graph, you need to follow these steps:
- Select a graph or diagram template that suits your data and purpose. In this case, you can use a line graph or a scatter plot to show the relationship between the number of shirts and the total cost.
- Add your data or information to the template. You can type in the numbers manually or upload an existing spreadsheet file.
- Add icons or illustrations from the library if you want to make your graph more appealing and informative.
- Customize your graph by changing the colors, fonts, labels, axes, legends, titles, and other elements. You can also apply different styles and themes to your graph.
- Download, share or print your graph as you wish. You can also embed it in other documents or presentations.
Here is an example of a line graph that shows the total cost of buying shirts for 0 through 15 shirts:
```markdown
# Total Cost of Buying Shirts
```code
| Number of Shirts | Total Cost ($) |
|------------------|----------------|
| 0 | 0 |
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
| 5 | 50 |
| 6 | 60 |
| 7 | 70 |
| 8 | 80 |
| 9 | 90 |
| 10 | 100 |
| 11 | 99 |
| 12 | 108 |
| 13 | 117 |
| 14 | 126 |
| 15 | 135 |
```
$$
y = \begin{cases}
10x & \text{if } x \leq 10 \\
9x + (10 - x) & \text{if } x > 10
\end{cases}
$$
a line graph with number of shirts on the x-axis and total cost on the y-axis
```
1 point) find a basis of the subspace of r3 r3 defined by the equation −3x1−3x2−8x3=0−3x1−3x2−8x3=0. basis: {{ ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥], ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥] }.
A basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}. This can be answered by the concept from Sets.
To find a basis of the subspace of R3 defined by the equation −3x1−3x2−8x3=0, we can first rearrange the equation as x3 = (-3/8)x1 - (3/8)x2.
Then we can rewrite the subspace as Span{{1,0,-3/8}, {0,1,-3/8}} since these two vectors span the subspace of solutions to the equation.
Therefore, a basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}.
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ravi made a shirt using 38 yards of green fabric and 13 yards of red fabric. how many yards of fabric did he use in all?
Ravi used a total of 51 yards of fabric for the shirt, 38 yards of green fabric, and 13 yards of red fabric.
Ravi used 38 yards of green fabric and 13 yards of red fabric to make a shirt. To find out the total yards of fabric used, you can simply add the two amounts together.
38 yards (green fabric) + 13 yards (red fabric) = 51 yards of fabric So, Ravi used a total of 51 yards of fabric for his shirt, Ravi made a shirt using 38 yards of green fabric and 13 yards of red fabric. how many yards of fabric
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