(a) The logistic regression model in this case is
log(p/(1-p)) = beta0 + beta1X1 + beta2X2 + beta3×X3
where p is the probability of Y-1 (i.e. getting a flu shot), X1 is the customer's age, X2 is the health awareness index, X3 is the gender (1 for men, 0 for women), and beta0, beta1 , beta2 , and beta3 are the estimated coefficients.
(b) From the output, the predictors that have the most influence on the response are X1, X2, and X3. You can confirm this by looking at the p-value of the Wald chi-square test for each predictor. A predictor is considered significant if the p-value is less than 0.05. In this case, the p-values for all three predictors are less than 0.05, indicating that they are all significant.
(c) AIC (Akaike Information Criterion) or SC (Schwarz Criterion) values can be used to determine if the overall model is significant. A lower AIC or SC value indicates a better fit of the model to the data. In this case, both the AIC and SC values are lower for the model with all three predictors (136.941 and 134.941, respectively) compared to the intercept-only model (140.010 and 136.941, respectively). This is significant because the model fits all three predictors better.
(d) These values can be incorporated into a logistic regression model to estimate the probability of Y-1 (getting a flu shot) with X1=60, X2=30, X3=1 (men) .
log(p/(1-p)) = beta0 + beta160 + beta230 + beta3*1
Solving for p gives:
p = 1/(1+exp(-log(p/(1-p))))
You can estimate p using the maximum likelihood estimates of beta0, beta1, beta2, and beta3 provided in the output.
(e) To determine the Y-1 odds ratio for men and women, you can compare the Y-1 odds for men (X3=1) and the Y-1 odds for women (X3=0). Men's Y-1 odds are as follows:
Odds (Y-1 for men) = p/(1-p)
where p is the Y-1 probability of her being male and can be estimated using a logistic regression model and maximum likelihood estimation of the coefficients. Women's Y-1 odds can be calculated in the same way using X3=0.
To create a 95% confidence interval for the odds ratio, use the standard error of the coefficient to calculate the standard error of the log odds ratio. A 95% confidence interval can be calculated as follows:
Odds ratio +/- 1.96×standard error
(f) To test whether the model containing only the intercept is significantly different from the model containing all three predictors, a likelihood ratio test can be used. The null hypothesis is that the model with only the intercept is not significantly different from the model with all three predictors. The alternative hypothesis is that the model with only the intercept is significantly different from the model with all three predictors. The test statistic is computed as
-2×(log probability
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If a solution calls for 1/4 cup vinegar mixed with 2 cups water , how many cups of vinegar goes into 27 total cups of solution?
A total of 3 cups of vinegar goes into 27 total cups
How to detemine the number of cups of vinegarFrom the question, we have the following parameters that can be used in our computation:
1/4 cups of vinegar
2 cups of water
So, we have
Water : Vinegar = 2 : 1/4
Rewrite as
Water : Vinegar = 8 : 1
Multiply by 3
Water : Vinegar = 24 : 3
The sum of 24 and 3 is 27
So, we have
Vinegar = 3
Hence, the number of cups of vinegar is 3
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A random sample of 115 observations results in 46 successes. Use Table 1.
a. Construct a 90% confidence interval for the population proportion of successes. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
b. Construct a 90% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
According to the question given,
Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.
The formula of a confidence interval that we will be using for the solution will be,
p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]
In the above expression,
p = observed population.
n = sample size
[tex]z_{a}[/tex] = critical value of confidence interval
Now the given observations in question = 115
That result in success = 46
The resultant sample proportion = [tex]\frac{46}{115}[/tex]
⇒ 0.40 and it is for both success and failure
Here we can see that the answer for both parts will be identical.
The critical value of z at 90% confidence = 1.64
a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.402
b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.598
Confidence interval = 0.402 to 0.598
Therefore,
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
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52% of 70
what is the answer
Answer: 36.4
Step-by-step explanation:
Just convert the percentage to decimal and multiply.
70 x 0.52 = 36.4
gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 16 feet high? recall that the volume of a right circular cone with height h and radius of the base r is given by v=(1/3)xpix(r^2)xh
The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.
We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.
V=pi*r^2*h/3 since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get
V=pi(h/2)^2*h/3 and if we simplify this, we get
V=pi*(h^3)/12
Now we need to take the derivative of both sides with respect to t
dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt
= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get
40 = pi * 16^2/4*dh/dt
dh/dt = 40 * 4 / ( 256 * pi )
= 40/(256*pi) ft/min,
= 10/64
= 5/32 ft/min
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Suppose that the daily number of miles driven per school bus driver in the United States is normally distributed with a mean of 300 mi and standard deviation equal to 26 mi. A local school bus budget committee believes the daily number of miles driven per bus driver in their community is different from 300 mi, but they are not sure if it is greater than or less than the national average.
To test their hypothesis, the committee chooses a random sample of 40 school bus drivers and records how many miles each of them drives per day during a typical week. On average, the bus drivers from the sample drive 309 mi per day. To test the hypothesis that the average number of miles driven by local bus drivers is different from the national average, the budget committee calculates the z-statistic to be 2.19 standard deviations above the population mean.
Use the standard normal z-distribution table to calculate the P-value that represents the probability of mistakenly rejecting the claim that the daily number of miles driven by local bus drivers is not statistically different from the national average. Give your answer as a decimal rounded to four places.
P-value:
The p-value for the z-distribution table is 0.4854.
What is z-distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given that the z statistic to be 2.19 standard deviation above the population mean.
2.19 can be written as 2.1 + 0.09
Z₂.₁₉ = Z₂.₁₊₀.₀₉ = 0.4854
Therefore p-value is 0.4854.
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Please help me with this question
The average rate change of the function is -4.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is f(x) = 1x² + 1x - 8.
Find the average rate change of the function in the interval [-4, -1]
For this compute the value of f(x) at x = -4 and x = -1.
Then find the difference the value of f(x) and divide it by the difference the value of x.
The average rate change of function f(x) in the interval [a,b] is [f(b) - f(a)]/(b-a).
Putting x = -4 in the given function:
f(-4) = 1(-4)² + 1(-4) - 8
f(-4) = 4
Putting x = -1 in the given function:
f(-1) = 1(-1)² + 1(-1) - 8
f(-1) = -8.
The rate change of x is -1 - (-4) = 3
The average rate change of the function is
[f(-1) - f(-4)] /3
= -8 - 4/3
= - 12/3
= -4
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60 POINTS!!! As a special promotion for its 12-ounce cans of cold coffee, a coffee drink company printed a message on the bottom of each can. Some of the bottoms read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in five wins a prize!" Suppose the company is telling the truth and that every 12-ounce can of coffee has a one-in-five chance of being a winner. Six friends each buy one 12-ounce can of coffee at a local convenience store. Let X equal the number of friends who win a prize.
Part A: Explain why X is a binomial random variable.
Part B: Find the mean and standard deviation of X. Interpret each value in context.
Part C: The store clerk is surprised when two of the friends win a prize. Is this group of friends just lucky, or is the company's one-in-five claim inaccurate? Compute P(X ≥ 2) and use the result to justify your answer.
A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established
B) The mean and standard deviation are respectively; 1.2 and 0.6
C) The probability given as P(X ≥ 2) is 0.34464
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCr * p^(x) * (1 - p)^(n - x)
where;
p = probability of "success"
n = number of trials, or the sample size
x = the number of "successes" in the probability we are trying to calculate.
A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.
Probability of success; p = 1/5
Number of events; n = 6 which is the random variable being binomial random variable:
There are two types of accomplishments: successes and failures.
Candies are unrelated to one another.
There is a set number of buddies available.
In addition, the chance of success is fixed.
Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.
B) The formula for the mean here is;
μ = np
Plugging in the relevant values gives;
μ = 6(1/5) = 1.2
Formula for the standard deviation is;
σ = √(np(1 - p))
Thus;
σ = √(6 * 1/5)(1 - (1/5)))
σ = 0.6
C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;
P(X ≥ 2) = 0.34464
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help!!
find the measures of each angle
The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24
What is centroid?Centroid is the point in a triangle where all the medians of the triangle intersects.
Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,
1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,
Therefore, 40°+y = 90°
y = 50°
x+y = 90°
x = 90°-50°
x = 40°
z = 180°-50° (linear pair)
z = 130°
2) we know that, the centroid divides the medians into 2:1
AY = 2YP
AY = 16
IY = TY/2
IY = 9
FG = GY+YF (segment addition postulate)
GY = YF/2
GY = 10
FG = 10+20 = 30
PA = AY+YP (segment addition postulate)
PA = 8+16
PA = 24
Hence. the measures are x, y and z are 40°, 50° and 130° and AY = 16, IY = 9, FG = 30, AP = 24
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Consider f(x) Equals StartFraction 8 (x minus 1) Over x squared + 2 x minus 3 EndFraction.
Which statements describe the existence of vertical asymptotes at x = –3 and x = 1?
At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = 2 and limit of f (x) as x approaches 1 plus = 2, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = infinity and limit of f (x) as x approaches negative 3 plus = negative infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = 2 and limit of f (x) as x approaches 1 plus = 2, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = infinity and limit of f (x) as x approaches 1 plus = infinity, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = infinity and limit of f (x) as x approaches negative 3 plus = negative infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = infinity and limit of f (x) as x approaches 1 plus = infinity, so there is no vertical asymptote.
The correct option that describes the vertical asymptote is; A: At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
f(x) = 8(x - 1)/(x² + 2x - 3)
Simplifying the denominator gives;
(x² + 2x - 3) = (x + 3)(x - 1)
Thus, our function is;
f(x) = 8(x - 1)/[(x + 3)(x - 1)]
(x - 1) will cancel out to give;
f(x) = 8/(x + 3)
Vertical asymptote:
Point in which the denominator is 0, so:
(x + 3) = 0
x = -3
Thus, we conclude that x = -3 is the vertical asymptote
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Drag and drop the choices into the boxes to correctly complete the table.
corresponding alternate interior alternate exterior none of these
Definitions:
Corresponding angles are the angles at matching corners.Alternate interior angles lie on the inner side of the parallel lines but on the opposite side of the transversal.Alternate exterior angles lie on the outer side of the parallel lines but on the opposite side of the transversal.The given angles are:
Top left figure ⇒ Alternate interiorTop middle figure ⇒ CorrespondingTop right figure ⇒ CorrespondingBottom left figure ⇒ Alternate exteriorBottom right figure ⇒ None of theseAwnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
Select the correct symbol.
9.48 ? 9.480
The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
What is meant by Inequality expressions?An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.
Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).
Given the incomplete expression
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
We are to fill it with the necessary inequality sign
For the expression:
1 1/4 × 2 1/5 = 5/4 * 11/5
1 1/4 × 2 1/5 = 55/20
1 1/4 × 2 1/5 = 2 3/4
For the expression 5/6 × 2 1/5
5/6 × 2 1/5 = 5/6 * 11/5
5/6 × 2 1/5 = 55/30
5/6 × 2 1/5 = 1 25/30
Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
The complete question is : Select the correct symbol to compare the expressions below.
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
Symbols: <, >, =
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Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. Number of fires x 69 58 47 84 62 57 72 Number of acres burned y 64 53 42 79 57 52 67 The correlation coefficient for the data is r=1 and α=0.05. Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. y′=a+bx a= Find y' when x=50
The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.
Straight line equation is y = a + bx.
The normal equations are
∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :
The values are calculated using the following table
x y x² x⋅y
58 62 3364 3596
47 51 2209 2397
84 88 7056 7392
62 66 3844 4092
57 61 3249 3477
72 76 5184 5472
69 73 4761 5037
hence :
∑x = 449
∑y = 477
∑x² = 29667
∑x⋅y = 31463
Substituting these values in the normal equations
7a+449b=477
449a+29667b=31463
Solving these two equations using Elimination method,
7a+449b=477
and 449a+29667b=31463
7a+449b=477→(1)
449a+29667b=31463→(2)
equation(1)×449
⇒3143a+201601b=214173
equation(2)×7
⇒3143a+207669b=220241
Substracting
⇒-6068b = -6068
⇒6068b = 6068
⇒b = 1
Putting b = 1 in equation (1), we have
7a+449(1) = 477
⇒7a = 477 - 449
⇒7a = 28 or a = 4.
Now Estimate y for x=50
y = a + bx , we get
y = 4 + 1×50
y = 4 + 50
y = 54
At x equals 50 we get the value of y as 54 .
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A. A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches.
If 25 items are chosen at random, what is the probability that their mean length is less than 17.4 inches?
Round to 4 decimal places
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.1 years, and standard deviation of 1.9 years.
If you randomly purchase 12 items, what is the probability that their mean life will be longer than 11 years?
Round to 4 decimal places.
B. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 98.4-cm and a standard deviation of 0.9-cm. For shipment, 15 steel rods are bundled together.
Find the probability that the average length of the rods in a randomly selected bundle is between 97.9-cm and 98.6-cm.
P(97.9-cm < X¯¯¯ < 98.6-cm) = Round to 4 decimal places.
The probability that their mean length is less than 17.4 inches is 28.26%
Given :
A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .
z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .
substitute the values
z = 17.4 - 19.7 / 4
= -2.3 / 4
= -0.575
P - value at z = -0.575 is 0.2826
Converting into percentage :
= 0.2826 * 100%
= 28.26 %
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Andreas has $18. Bonnie has 1 2/3 times as much as Andreas. Cheryl has 1 3/5 times as much as Bonnie.
How much money do
they have altogether?
I'm not sure what the reasoning is
The reasons that complete the statements are:
Statement 2: GivenStatement 4: SAS congruence propertyHow to determine the reasons that complete the statementsFrom the question, we have the following parameters that can be used in our computation:
Triangles = RST, and TUR
From the question, we have the following given parameters
∠SRT ≅ ∠UTR
This means that
Statement 2: ∠SRT ≅ ∠UTR ------ Given
At this point, we have
RS ≅ TU --- Congruent side (S)
∠SRT ≅ ∠UTR ------ Congruent angle (A)
RT ≅ TR --- Congruent side (S)
When these congruent sides and angles are combined, we have
SAS congruence property
The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent
Hence, the additional information on the congruency of the triangles are Given and SAS congruence property
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Data is collected from the US Geologic Survey about the flow rate of the Poudre river. After some study, and unit conversions, a scientist makes a first model of the historical flow rate data as F(t) = 1.5 + 1.2 cos(2 t) in billions of cubic feet per year, while t is measured in fractions of a year since May 1, 2000. Use the Fundamental Theorem of Calculus to find the net amount of water from t = 0) to t = using this flow rate F"(t).First, F(t) = +C The model predicts the net amount of water discharged from the Poudre is F112 -Filo 0.75 What does the model predict the net discharge will be from t = 0 to t = 12 Net discharge = 1.5 Billions of ft 3
The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.
The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.
In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:
Net discharge = F(12) - F(0)
= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))
= 1.5 + 1.2 cos(24) - 1.5 - 1.2
= -0.8 + 1.2 cos(24)
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Suppose that in an election voter preference is sharply divided along gender lines. 60% of women will vote for Candidate J, the rest will vote for Candidate K; 30% of men will vote for Candidate J, the rest for Candidate K. Which of the following represents the lowest percentage of voters that must be women on election day, in order that Candidate J wins the election?
* 65%
* 67%
* 69%
* 71%
* 73%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
What exactly is a ratio ?A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.
The percentage of voters who select Candidate J is:
60% of x are voters are female
30% of (1 - x), who vote are male
If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:
0.6x + 0.3(1 - x) > 0.5
0.6x + 0.3 - 0.3x > 0.5
0.3x > 0.2
x > 2/3
x > 0.667
x > 67%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
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determine the number of different sets of quantum numbers possible for each of the following shells. n2
Answer:
Step-by-step explanation:
Explanation:
As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.
This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.
As you know, the number of orbitals you get per energy level is given by the equation
no. of orbitals
=
n
2
, where
n
- the principal quantum number, the ones that gives the energy level.
So, if you're dealing with the third energy level, you can say that it will contain a total of
no. of orbitals
=
3
2
=
9
distinct orbitals.
Now, each orbital can contain a maximum of
2
electrons of opposite spins. This means that the third energy level will contain a maximum number of
no. of electron
=
9
⋅
2
=
18 e
−
So, if each electron is described by an unique set of quantum numbers, you can conclude that
18
sets of quantum numbers are possible for the third energy level.
ok maybe that will help!
e the problem.
1) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The
teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the next 42%. What is the
bottom cutoff for a C grade? Round your answer to the nearest whole number..
A) 68
B) 63
C) 77
D) 65
z = -1.34 < (a - 70)/9
And if we solve for we got
a = 70 - 1.34 * 9 = 57.95 = 98
So, the value of height that separates the bottom 9% of data from the top 91% is 58.
And the answer for this case would be:
a) 58
What is the Normal distribution and Z-score?
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The solution to the problem
Let X be the random variable that represents the scores of a population, and for this case we know the distribution for X is given by:
X ~ N (70, 9)
Where μ = 70, and σ = 9
For this case, the figure attached illustrates the situation for this case.
We know from the figure that the lower limit for D accumulates 9% or 0.09 of the area below and 0.91 or 91% of the area above.
we want to find a value a, such that we satisfy this condition:
P(X > a) = 0.91 (a)
P(X < a) = 0.09 (b)
Both conditions are equivalent in this case. We can use the z score again in order to find the value a.
As we can see in the figure attached the z value that satisfies the condition with 0.09 of the area on the left and 0.91 of the area on the right it's z=-1.34. On this case P(Z<-1.34)=0.09 and P(z>-1.34)=0.91
If we use condition (b) from the previous we have this:
P(X < a) = P(X - μ)/σ < (a - μ)/σ) = 0.09
P(z < (a - μ)/σ) = 0.09
But we know which value of z satisfies the previous equation so then we can do this:
z = -1.34 < (a - 70)/9
And if we solve for we got
a = 70 - 1.34 * 9 = 57.95 = 98
Hence, the value of height that separates the bottom 9% of data from the top 91% is 58.
And the answer for this case would be:
a) 58
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3. Which of the following is the solution to lx + 12| = 3x.
A. x = 3
C. x = 6
b. x = -6
d. x = - 3
2. Of the total pounds, x, of fudge at the fudge shop on Monday morning, {3}/{4} contain nuts. Helena works at the fudge shop and prepares 12 {3}/{4} more pounds of fudge containing nuts to fulfill a special order Monday afternoon. With this additional amount of fudge, there are at least 29 {5}/{8} pounds of fudge containing nuts at the fudge shop on Monday.
(a) Write an inequality that represents the scenario. Begin by defining your variable.
(b) Solve your inequality from Part (a). Show all work.
(c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge shop Monday morning?
Answer:
At least means less than or equal to.
Fewest means the smallest number of boxes.
12 3/4 +x ≥ 29 5/8
x ≥ 16 7/8
The fewest number of boxes would be almost ≅ 42 boxes
Part A:
Let x denote the amount of fudge at the shop.
Helena prepares 12 3/4 pounds of fudge containing nuts.
Mathematically, the total amount of fudge on Monday will be
12 3/4 +x
Of this amount of fudge there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday
12 3/4 +x ≥ 29 5/8
Part B:
The inequality can be solved
12 3/4 +x ≥ 29 5/8
x ≥ 29 5/8- 12 3/4
x ≥ 29- 12 5/8- 3/4
The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.
x ≥ 17 (5-6)/8
x ≥ 17 - 1/8
x ≥ (136-1)/8
x ≥ (135)/8
x ≥ 16 7/8
Part C :
To find the number of boxes we divide the equal number of pounds .
12 3/4 + 29 5/8
12 + 29 3/4 + 5/8
41 11/8
42 3/8
The fewest number of boxes would be almost ≅ 42 boxes
At least problem can be understood by the following link.
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When you are testing hypotheses by using proportions, what are the necessary requirements? OA. np 25 and nq 25 ?B.np < 5 and nq < 5 C. The population standard deviation is unknown. D. p
The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5
To test hypotheses using proportions, the following requirements are necessary:
np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.
The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.
This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.
Hence, the correct answer would be an option (A).
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Can someone please explain step by step on how I stole this problem?
-1 - ( -0.25 )
The final answer of the problem is -0.75.
What is the order of operations?
The order of operations is also known as the hierarchy of operations. The order of operations tells us the order in which we should perform mathematical operations in order to get the correct result. The order of operations is usually represented by the acronym PEMDAS:
P: Parentheses first
E: Exponents (ie Powers and Square Roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)
We have,
-1 - (-0.25)
Using the order of operations, we can solve this problem as follows:
Parentheses: The first step is to perform any calculations inside parentheses. In this case, there are no parentheses, so we can move on to the next step.
Exponents: There are no exponents in this problem, so we can move on to the next step.
Multiplication and Division: There is no multiplication or division in this problem, so we can move on to the next step.
Addition and Subtraction: Finally, we can perform addition and subtraction in the problem. We start from left to right, so we start with the first operation: -1 - (-0.25). To subtract a negative number, we can use the rule that subtracting a negative number is the same as adding a positive number.
Therefore, we have -1 + 0.25.
The final step is to simplify the expression by performing the addition: -1 + 0.25 = -0.75.
Therefore, the final result of the problem is -0.75.
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A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, how long will it take the student to complete the project?
The number of hours it will take the student to complete the project is 5 / 6 hours.
How to find the time the project will be completed?A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, the time it will take the student to complete the project can be calculated as follows:
Therefore,
let
x = time it will take the student to complete the project
Hence
if 4 / 5 x = 2 / 3 hours
x = ? hours
cross multiply
Therefore,
number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x
number of hours to complete the whole math project = 2 / 3 x × 5 / 4x
number of hours to complete the whole math project = 10x / 12x
number of hours to complete the whole math project = 10 / 12
number of hours to complete the whole math project = 5 / 6 hours
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Dae and Eric are working together on a paper. Dae typed 333 words in 9 minutes, and Eric typed 252 words in 6 minutes. How many more words per minute did Eric type?
Eric typed 15 words more than Dae per minute.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
To find the amount of words typed in 1 minute for both;
Dae = 333/9
Dae = 27 words per minute
Eric = 252/6
Eric = 42 words per minute
Therefore 42 - 27 = 15 words per minute
Eric typed 15 more words per minute.
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Which points have a distance of 6 units between them?
Select all that apply.
A-(-12,2) and B-(-6,2)
B-(-6,2) and C-(-6-4)
C-(-6-4) and D-(6,2)
D-(6.2) and E=(6,4)
E-(64) and F=(-12.4) please help me with this
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
Distance between two points:The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by
Distance PQ = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]Here we have
A (-12, 2) and B(-6, 2)
B (-6, 2) and C(-6, -4)
C (-6, -4) and D(6, 2)
D (6, 2) and E(6, 4)
E (6, 4) and F(-12, 4)
Here we will find the distance between given points to find the point which has 6 units between them.
As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]
For Option A
A (-12, 2) and B(-6, 2)
Distance = √(-6 + 12)² + (2 - 2)²
= √[(6)² + (0)²] = √36 = 6
For Option B
For B (-6, 2) and C(-6, -4)
Distance = √(-6 - (-6))² + ( - 4 - 2)²
= √[(0)² + (-6)²] = √36 = 6
For Option C
For C (-6, -4) and D(6, 2)
Distance =√(6 - (-6))² + (2 - (-4))²
= √(12)² + (6)² = √180 = 6√5
For Option D
For D (6, 2) and E(6, 4)
Distance = √(4 - 2)² + ( 6 - 6)²
= √[(2)² + (0)²] = √4 = 2
For Option E
For E (6, 4) and F(-12, 4)
Distance = √(-12 - 6)² + (4 - 4)²
= √[(18)² + (0)²] = √18² = 18
Therefore,
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
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Solve
y=-2 x
y=-9 x+21
Answer:
X = 3, Y = -6
Step-by-step explanation:
y = -2x
y = -9x + 21
Bring Y and X on the same side (alone).
0 = -2x – y
-21 = -9x – y
Multiply the top equation by -1 so we can cancel out y later on (to make it easier to solve for x).
0 = 2x + y
-21 = -9x – y
Add the equations.
-21 = -7x
Divide by -7.
X = 3
Solve for Y and check.
Y = -2(3)
Y = -6
Use the other equation to make sure.
(-6) = -9(3) + 21
-6 = -27 + 21
Have a nice day :D
Label a ray with endpoint Y. Determine an appropriate name for a ray whose endpoint is Y. Choose the correct ray whose endpoint is Y. A. Y X B. X Y C. X Y D. Y x Choose an appropriate name for a ray whose endpoint is Y. A. XY B. XY C. YX
Label a ray with endpoint Y. An appropriate name for a ray whose endpoint is XY displays a ray with the endpoint Y.
A line with a single defined endpoint that continuously moves away from another is known as a ray (endpoint B in this case).
A segment of a line that lacks an endpoint but has a specified starting point. It can go on forever in a single direction. A ray cannot be measured since it has no end point.
In mathematics, a ray is a segment of a line with a definite starting point but no ending. It can go on forever in a single direction. A ray cannot be measured since it has no end point. Two rays with the same terminal are united to form an angle. The vertex of the angle is referred to as the common endpoint of the rays, while the sides of the angle are referred to as the rays themselves.
The ray in the hypothetical situation has one endpoint B and an endlessly extending endpoint A. (as shown by the arrowhead).
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Review 2 HW Jack and Jill compare their monthly text plans. Jack's plan cost $9.00 plus $0.30 per text. Jills plan cost $0.60 per text. The equations below show the cost, c for each plan depending on how many texts, t, are sent Jack's Plan: c = 0.30t+9 Jills's Plan: c = 0.60t In one month, Jack and Jill paid the same amout. Enter the number of text messages the each sent.
Jack's plan: c=0.30t+9
Jill's plan: c=0.60t
I one month, Jack and Jill paid the same amount. enter the number of text messages they each sent
Answer: To solve this problem, we need to set the two equations equal to each other and solve for the number of text messages that were sent by each person. We know that the cost of Jack's plan is c = 0.30t + 9 and the cost of Jill's plan is c = 0.60t. To find the number of text messages they each sent, we can set these two equations equal to each other and solve for t:
0.30t + 9 = 0.60t
0.30t = 0.60t - 9
0.30t = 0.60t - 9
-0.30t = -9
t = 30
Therefore, if Jack and Jill paid the same amount for their text plans, they each sent 30 text messages.
