Solve for q. √3q + 2 = √5

Multiple linear regression can be said to be a statistical technique that uses several explanatory variables to predict the outcome of a response variable.

The Formula for Multiple Linear Regression Is

yi= β0+β1xi1+β2xi2+...+βpxip+ϵ

​

where, for i=n observations

yi​= Dependent variable

xi​= Expanatory variable

β0​= y - intercept (constant term)

βp​= Slope coefficients for each explanatory variable

ϵ= The model’s error term (also known as the residuals)​

From the question written above,

yi= weight gain which is dependent on the explanatory variables which are hemoglobin change, tap water consumption, and age. i.e. xi

Model assumptions

1. There is a linear relationship between the dependent variables and the independent variables.

2. The independent variables are not too highly correlated with each other.

3. yi observations are selected independently and randomly from the population.

4. Residuals should be normally distributed with a mean of 0 and variance σ.

(Investopedia, 2019)

Answer:

Yes, Tom must be admitted to this university.

Step-by-step explanation:

We are given that the scores on national test are normally distributed with a mean of 500 and a standard deviation of 100.

Also, we are provided with the condition that Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test.

Let, X = score in national test, so X ~ N([tex]\mu=500 , \sigma^{2} = 100^{2}[/tex])

The standard normal z distribution is given by;

              Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Now, z score of probability that tom scores 585 is;

             Z = [tex]\frac{585-500}{100}[/tex] = 0.85

Now, proportion of students scoring below 85% marks is given by;

P(Z < 0.85) = 0.80234

This shows that Tom scored 80.23% of the students who took test while he just have to score more than 70%.

So, it means that Tom must be admitted to this university.

Answer:

The standard error for the mean finish time of 30 randomly selected participants is 0.055 hours

Step-by-step explanation:

Standard error = sample standard deviation ÷ sqrt (sample size)

sample standard deviation = 0.30 hours

sample size = 30

standard error = 0.30 ÷ sqrt(30) = 0.30 ÷ 5.477 = 0.055 hours

Answer:

a) 0.9961

b) 0.9886          

Step-by-step explanation:

We are given the following information:

We treat passenger not showing up as a success.

P(passenger not showing up) = 0.10

Then the number of passengers follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 125

a) probability that every passenger who shows up can take the flight

[tex]P(x \geq 5) = 1- P(x = 0) - P(x = 1)-P(x = 2) - P(x = 3) - P(x = 4) \\= 1-\binom{125}{0}(0.10)^0(1-0.10)^{125} -...-\binom{125}{4}(0.10)^4(1-0.10)^{121}\\=0.9961[/tex]

b)  probability that the flight departs with empty seats

[tex]P(x > 5) =P(x\geq 5) - P(x = 5) \\= 0.9961 -\binom{125}{5}(0.10)^5(1-0.10)^{120}\\=0.9961-0.0075\\ = 0.9886[/tex]

a. By the law of total probability,

[tex]P(E)=P(A_1\cap E)+P(A_2\cap E)+P(A_3\cap E)[/tex]

and using the definition of conditional probability we can expand the probabilities of intersection as

[tex]P(E)=P(E\mid A_1)P(A_1)+P(E\mid A_2)P(A_2)+P(E\mid A_3)P(A_3)[/tex]

[tex]P(E)=0.1\cdot0.3+0.6\cdot0.5+0.8\cdot0.2=0.49[/tex]

b. Using Bayes' theorem (or just the definition of conditional probability), we have

[tex]P(A_1\mid E)=\dfrac{P(A_1\cap E)}{P(E)}=\dfrac{P(E\mid A_1)P(A_1)}{P(E)}[/tex]

[tex]P(A_1\mid E)=\dfrac{0.1\cdot0.3}{0.49}\approx0.0612[/tex]

c. Same reasoning as in (b):

[tex]P(A_2\mid E)=\dfrac{P(E\mid A_2)P(A_2)}{P(E)}\approx0.612[/tex]

d. Same as before:

[tex]P(A_3\mid E)=\dfrac{P(E\mid A_3)P(A_3)}{P(E)}\approx0.327[/tex]

(Notice how the probabilities conditioned on [tex]E[/tex] add up to 1)

Answer:

0.0904 or 9.04%

Step-by-step explanation:

Mean glucose (μ) = 93.5

Standard deviation (σ) = 19.8

In a normal distribution, the z-score for any glucose value, X, is given by:

[tex]Z= \frac{X-\mu}{\sigma}[/tex]

For X = 120, the z-score is:

[tex]Z= \frac{120-93.5}{19.8}\\ Z=1.3384[/tex]

A z-score of 1.3384 corresponds to the 90.96th percentile of a normal distribution. Therefore, the probability that glucose exceeds 120 in this population is:

[tex]P(X>120) = 1-0.9096=0.0904 = 9.04\%[/tex]

Answer:

Probability that glucose exceeds 120 in this population is 0.09012.

Step-by-step explanation:

We are given that in a population of adults between the ages of 18 and 49, glucose follows a normal distribution with a mean of 93.5 and standard deviation of 19.8, i.e.; [tex]\mu[/tex] = 93.5  and  [tex]\sigma[/tex] = 19.8 .

Let X = amount of glucose i.e. X ~ N([tex]\mu = 93.5 , \sigma^{2} = 19.8^{2}[/tex])

Now, the Z score probability is given by;

           Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

So,Probability that glucose exceeds 120 in this population =P(X>120)

P(X > 120) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{120-93.5}{19.8}[/tex] ) = P(Z > 1.34) = 1 - P(Z <= 1.34)

                                                   = 1 - 0.90988 = 0.09012 .

Answer:

Sew attachment for xomplete solution and answer

Step-by-step explanation:

Given that;

Suppose that f is a continuous function and that −24 ≤ f 00(x) ≤ 3 for 0 ≤ x ≤ 1. If the Midpoint Rule of order n, namely Mn, is used to approximate R 1 0 f(x) dx, how large must n be to guarantee that the absolute error in using Mn ≈ R 1 0 f(x) dx is less than 1/100

See attachment

Answer:

The service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).                    

Step-by-step explanation:

The drug J9263 Eloxatin contains 0.5 mg oxaliplatain.

For a infusion of 50 mg the unit reported for service line information is:

- Service line: J9263 x 100

- Unit reported for service line information: 50 = 100 x 0.5 mg

Hence, for a infusion of 150 mg, the unit reported for service line information is:

- Unit reported: 150(300 x 0.5 mg = 150)

- Service line information: J9263 x 300

Therefore, if the physician provided 150 mg infusion of the drug instead of an injection the service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).

I hope it helps you!                          

The unit reported for service line information for 150 mg infusion based on the injection description is :

Given the injection description :

For 150 mg infusion :

Unit reported would be:

Therefore, the service line information and the unit reported would be:

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Answer:

Step-by-step explanation:

                    1

                1      1

            1      2      1

         1     3      3      1

      1    4     6       4       1

   1   5    10     10       5     1

 1    6   15   20      15    6     1

1    6   15   20      15    6     1

we use these for the expansion of (5x² + 2y³)⁶

1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+  15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶

78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸

a.)a = 6, b = 9. the coefficient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000

b) a = 2, b = 15. the coefficient of xᵃyᵇ ( 960x²y¹⁵) = 960

c) a = 3, b = 12. the coefficient of xᵃyᵇ is not present

d) a = 12, b = 0 the coefficient of xᵃyᵇ ( 78125ₓ¹²)  = 78125

e) a = 8, b = 9. the coefficient of xᵃyᵇ is not present

The coefficients of xᵃyᵇ for respective given values of a and b have been provided below.

We are given the expression;

(5x² + 2y³)⁶

Using online binomial expansion calculator gives us;

15625x¹² + 37500x¹⁰y³ + 37500x⁸y⁶ + 20000x⁶y⁹ + 6000x⁴y¹² + 960x²y¹⁵ + 64y¹⁸

We want to find the coefficient of xᵃyᵇ in the binomial expansion;

1) When a = 6 and b = 9, the coefficient is 20000

2) When a = 2, b = 15; the coefficient is 960

3) When a = 3 and b = 12; there is no coefficient

4) When a = 12 and b = 0; the coefficient is 15625

5) When a = 8 and b = 9; there is no coefficient.

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When [tex]x=3[/tex], we get the parabola

[tex]z=-4-2y^2[/tex]

We can parameterize this parabola by

[tex]\vec r(t)=(3,t,-4-2t^2)[/tex]

Then the tangent vector to this parabola is

[tex]\vec T(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=(0,1,-4t)[/tex]

We get the point (3, 2, -12) when [tex]t=2[/tex], for which the tangent vector is

[tex]\vec T(2)=(0,1,-8)[/tex]

Then the line tangent to the parabola at [tex]t=2[/tex] passing through the point (3, 2, -12) has vector equation

[tex]\ell(t)=(3,2,-12)+t(0,1,-8)=(3,2+t,-12-8t)[/tex]

which in parametric form is

[tex]\begin{cases}x(t)=3\\y(t)=2+t\\z(t)=-12-8t\end{cases}[/tex]

for [tex]t\in\Bbb R[/tex].

The parametric equation of the tangent line is [tex]L(t)=(3,2+t,-12-8t)[/tex]

The equation of Paraboloid is,

                 [tex]z =8-x-x^{2} -2y^{2}[/tex]

Equation of parabola when [tex]x = 3[/tex] is,

       [tex]z=8-3-3^{2} -2y^{2} \\\\z=-4-2y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(3,t,-4-2t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-4t)[/tex]

We get, the point [tex](3, 2, -12)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-8)[/tex]

So that, the tangent line to this parabola at the point (3, 2, −12) will be,

     [tex]L(t)=(3,2,-12)+t(0,1,-8)\\\\L(t)=(3,2+t,-12-8t)[/tex]

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"You do not eat tofu" is derived using the Modus Tollens rule of inference.

The rule of inference that is used to derive the conclusion "You do not eat tofu" from the given statements is Modus Tollens.

Modus Tollens is a valid deductive argument form that follows this structure:

1. If P, then Q.

2. Not Q.

3. Therefore, not P.

The statements correspond to:

1. For all x, if x is healthy to eat, then x does not taste good.

2. Tofu is healthy to eat.

3. You only eat what tastes good.

Using these statements, we can infer:

1. If tofu is healthy to eat, then tofu does not taste good. (From statement 1)

2. Tofu does not taste good. (From statement 2 and the derived inference)

3. Therefore, you do not eat tofu. (Using Modus Tollens with statement 3 and the derived inference)

So, the conclusion "You do not eat tofu" is derived using the Modus Tollens rule of inference.

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Final answer:

The rule of inference used to derive the conclusion 'You do not eat tofu' is called Modus Tollens, which allows to deduce that if 'p implies q' is true and 'q' is false, then 'p' must also be false.

Explanation:

The student is asking about a logical inference rule used to derive a conclusion from a set of premises. Considering the provided statements, which can be summarized as:

For all x, if x is healthy to eat, then x does not taste good (All healthy foods taste bad).

Tofu is healthy to eat.

You only eat what tastes good.

We can see that the rule of inference used here is Modus Tollens. This rule of inference suggests that if we have a conditional statement (if p then q) and it is given that the consequent q is false (not q), then the antecedent p must also be false (not p).

To apply Modus Tollens:

Translate the given information into logical statements:
a) If something is healthy (p) then it does not taste good (q).
b) Tofu is healthy (p).
c) You do not eat what does not taste good (¬q).

Since tofu is healthy (p), it does not taste good as per the given rule (therefore, q is true). But the third statement says you do not eat what does not taste good, meaning (¬q). If (¬q) is valid, then by Modus Tollens, you do not eat tofu (¬p).

Thus, the usage of Modus Tollens allows us to infer that 'You do not eat tofu' from the given premises.

Answer:

81.2 is the 62th percentile

Step-by-step explanation:

What is the interpretation for a percentile?

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.

So

[tex]p = \frac{186}{300} = 0.62[/tex]

81.2 is the 62th percentile

Answer:

For k = 6 or k = -6, the equation will have exactly one solution.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

If [tex]\bigtriangleup = 0[/tex], the equation has only one solution.

In this problem, we have that:

[tex]3x^{2} + kx + 3 = 0[/tex]

So

[tex]a = 3, b = k, c = 3[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

[tex]\bigtriangleup = k^{2} - 4*3*3[/tex]

[tex]\bigtriangleup = k^{2} - 36[/tex]

We will only have one solution if [tex]\bigtriangleup = 0[/tex]. So

[tex]\bigtriangleup = 0[/tex]

[tex]k^{2} - 36 = 0[/tex]

[tex]k^{2} = 36[/tex]

[tex]k = \pm \sqrt{36}[/tex]

[tex]k = \pm 6[/tex]

For k = 6 or k = -6, the equation will have exactly one solution.

Answer:

Independent Events

Step-by-step explanation:

Two events are mutually exclusive or disjoint if they cannot both occur at the same time.

Two events are independent if the probability of occurrence of one does not affect the probability of occurrence of the other.

The complement of any event B is the event [not B], i.e. the event that B does not occur.

Australia plays Argentina for the championship in the Rugby World Cup.

At the same time, Ukraine plays Russia for the World Team Chess Championship.

A = event that Argentina wins their rugby match.

B = the event that Ukraine wins their chess match.

The two events A and B are Independent as the outcome of one does not affect the outcome of the other

Answer:

See explanation to get answer.

Step-by-step explanation:

Solution

As per the data and information given in the question, there are three Bidders, one each on Monday, Tuesday and Wednesday.

Bidder 1 may bid on Monday either for $2,000,000 or $3,000,000 with probabilities 0.5 each

Therefore expected pay-off for Bidder 1 is $2,500,000 (2,000,000*.52 + 3,000,000*.5)

Bidder 2 may bid on Tuesday either for $2,000,000 with probability 0.9 or $4,000,000 with probability 0.1

Therefore expected pay-off for Bidder 2 is $2,200,000 (2,000,000*.9 + 4,000,000*.1)

Bidder 3 may bid on Wednesday either for $1,000,000 with probability 0.7 or for $4,000,000 with probability 0.3

Therefore expected pay-off for Bidder 3 is $1,900,000 (1,000,000*.7 + 4,000,000*.3)

Based on the comparison of the above mentioned calculations for the expected pay-off for the bidders, it is recommended that the optimal decision strategy among the bidders is to go for Bidder 1 with highest expected pay-off of $2,500,000 and accept the bid of Bidder 1.

Risk profile for the optimal solution is $2,000,000 with probability 0.5 and $3,000,000 with probability 0.5

Bid may be for $4,000,000 with probability of 0.1 by Bidder 2 or with probability 0.3 by Bidder 3

Answer:

The z statistic is 0.23.

Step-by-step explanation:

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 104 mg

population mean (mu) = 100 mg

sd = 55 mg

n = 10

z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23

Final answer:

The z-statistic for the given hypothesis test is calculated based on the sample mean, population standard deviation, and sample size.

Explanation:

The z-statistic for this hypothesis test can be calculated using the sample mean, population standard deviation, and sample size.

Given that the sample mean is 104 mg, population standard deviation is 55 mg, and sample size is 10 pills, the z-statistic is calculated as (104 - 100) / (55 / sqrt(10)), which equals 0.8.

Therefore, the correct z-statistic for this scenario is 0.80.

Answer:

d. -1.9; not unusual

Step-by-step explanation:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that;

[tex]X = 50, \mu = 69, \sigma = 10[/tex].

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{50 - 69}{10}[/tex]

[tex]Z = -1.9[/tex]

A z-score of -1.9 is higher than -2 and lower than 2, so it is not unusual.

So the correct answer is:

d. -1.9; not unusual

Answer:

The relation represents y as a function of x, because each value of x is associated with a single value of y.

Answer:

A) P(A⋂B) = 0.35

B) P(A⋃B)= 0.53

C) P(A⋂B′) = 0.08

D) P(A|B) = 0.778

Step-by-step explanation:

We know the following from the question:

- Let Proportion of Americans who expect to save more money next year than they saved last year be

P(A) and its = 0.43

-Let proportion who plan to reduce debt next year be P(B) and it's =0.81

A) probability that this person expects to save more money next year and plans to reduce debt next year which is; P(A⋂B) = 0.43 x 0.81 = 0.348 approximately 0.35

B) probability that this person expects to save more money next year or plans to reduce debt next year which is;

P(A⋃B)= P(A) + P(B) − P(A⋂B)

So, P(A⋃B)= 0.43 + 0.45 − 0.35 = 0.53

C). Probability that this person expects to save more money next year and does not plan to reduce debt next year which is;

P(A⋂B′) = P(A) − P(A⋂B)

P(A⋂B′) =0.43 − 0.35 = 0.08

D) Probability that this person does not expect to save more money given that he/she does plan to reduce debt next year which is;

P(A|B) = [P(A⋂B)] / P(B)

So P(A|B) =0.35/0.45 = 0.778

The probabilities for the given scenarios are as follows: a. 34.93%, b. 53.07%, c. 8.07%, and d. 126.67%.

a. To find the probability that a person expects to save more money next year and plans to reduce debt next year, we need to multiply the probabilities of both events occurring. The probability that a person expects to save more money next year is 43%, and of those who expect to save more money next year, 81% plan to reduce debt. Therefore, the probability is 0.43  imes 0.81 = 0.3493, or 34.93%.

b. To find the probability that a person expects to save more money next year or plans to reduce debt next year, we can add the probabilities of both events occurring and subtract the probability of both events occurring at the same time (found in part a). The probability of expecting to save more money next year is 43%, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.43 + 0.45 - 0.3493 = 0.5307, or 53.07%.

c. To find the probability that a person expects to save more money next year and does not plan to reduce debt next year, we subtract the probability from part a from the probability of expecting to save more money next year. The probability of expecting to save more money next year is 43%, and the probability of both expecting to save more money and planning to reduce debt is 34.93%. Therefore, the probability is 0.43 - 0.3493 = 0.0807, or 8.07%.

d. To find the probability that a person does not expect to save more money given that he/she does plan to reduce debt next year, we need to divide the probability of not expecting to save more money by the probability of planning to reduce debt next year. The probability of not expecting to save more money is 1 - 0.43 = 0.57, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.57 / 0.45 = 1.2667, or 126.67%.

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To find the probability of different scenarios involving defective components produced by a certain process, we can use the Poisson and binomial distributions.

(a) To find the probability that exactly 15 defective components are produced, we can use the formula for the Poisson distribution:

P(X=k) = (e^(-λ) * λ^k) / k!

Here, λ is the mean number of defective components produced in one day, which is 20. So, λ = 20. Substituting this value into the formula, we get:

P(X=15) = (e^(-20) * 20^15) / 15!

Calculating this expression will give us the probability.

(b) To find the probability that exactly 10 of the 15 defective components are repairable, we can use the binomial distribution since each defective component has a fixed probability of being repairable. Here, the number of trials is 15, and the probability of success (being repairable) is 0.60. Substituting these values into the binomial distribution formula, we can calculate the probability.

(c) Given the value of N, the number of defective components produced, X has a binomial distribution since X represents the number of repairable defective components. The probability of each component being repairable is constant, so it follows a binomial distribution.

(d) To find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, we can multiply the probabilities obtained from parts (a) and (b) together, since these events are independent. Multiplying the results will give us the desired probability.

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(a) The probability that exactly 15 defective components are produced is 0.0516

(b) Given that exactly 15 defective components are produced, the probability that exactly 10 of them are repairable is 0.1241.

(c) Given the value of N, X follows a binomial distribution

(d) The probability that exactly 15 defective components are produced, with exactly 10 of them being repairable is 0.0064.

(a) Probability of Exactly 15 Defective Components

A Poisson distribution with mean λ = 20 is used. The formula is:

[tex]P(X = k) = (e^{(-\lambda)} * \lambda^k) / k![/tex]

For k = 15 and λ = 20:

[tex]P(X = k) = (e^{(-20)} * 20^15) / 15! \approx 0.0516[/tex]

(b) Probability that Exactly 10 Out of 15 Defective Components are Repairable

This scenario uses a binomial distribution.

Given N = 15 defectives, the probability that exactly 10 are repairable (with p = 0.60) is:

[tex]P(X = 10 | N = 15) = C(15,10) * 0.6^{10} * 0.4^{5} \approx 0.1241[/tex]

(c) Distribution of X Given N

Given N = n

X (number of repairable components) follows a binomial distribution Bin(n, 0.60).

So, X | N = n follows Bin(n, 0.60).

(d) Probability of 15 Defective Components with Exactly 10 being Repairable

The joint probability is the product of the Poisson and binomial probabilities:

[tex]P(X = 15) * P(Y = 10 | X = 15)= 0.0516 * 0.1241 \approx 0.0064[/tex]

Answer:

0.717 or 71.7%

Step-by-step explanation:

P(M) = 0.852

P(D) = 0.759

P(M or D) = 0.894

The probability that a randomly selected American has both medical and dental insurance is given by the probability of having medical insurance, added to the probability of having dental insurance, minus the probability of having either insurance:

[tex]P(M\ and\ D) = P(M)+P(D)-P(M\ or\ D)\\P(M\ and\ D) =0.852+0.759-0.894\\P(M\ and\ D) =0.717=71.7\%[/tex]

The probability is 0.717 or 71.7%.

The result is a 71.7% probability of an adult American having both insurances.

The question revolves around finding the probability of a randomly selected adult American having both medical and dental insurance. To calculate this, we use the principle of inclusion-exclusion. According to the problem statement, the percentage of adults with medical insurance is 85.2%, with dental insurance is 75.9%, and with either of the two is 89.4%. The principle of inclusion-exclusion states that the probability of the union of two events (medical or dental insurance) is equal to the sum of the probabilities of each event minus the probability of their intersection (both insurances).

Let's denote the following:

Using the principle of inclusion-exclusion, we find P(Medical and Dental) as follows:

P(Medical and Dental) = P(Medical) + P(Dental) - P(Medical or Dental)

P(Medical and Dental) = 85.2% + 75.9% - 89.4%

P(Medical and Dental) = 160.1% - 89.4%

P(Medical and Dental) = 71.7%

Therefore, the probability that a randomly selected adult American will have both medical and dental insurance is 71.7%.

Answer:

Mean = 94

Standard deviation = 1.12

The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]\mu = 94, \sigma = 10[/tex]

By the Central Limit Theorem

The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.

Mean = 94

Standard deviation:

[tex]s = \frac{10}{\sqrt{80}} = 1.12[/tex]

Answer:

The value of [tex]\bar d[/tex] is -0.2.

The value of [tex]s_{\bar d}[/tex] is 0.3464.

[tex]\mu_{d}[/tex] = mean difference in body temperatures.

Step-by-step explanation:

The data for body temperatures from five different subjects measured at 8 AM and again at 12 AM are provided.

The formula of [tex]\bar d[/tex] and [tex]s_{\bar d}[/tex] are:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})[/tex]

[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}[/tex]

Consider the table below.

Compute the value of [tex]\bar d[/tex] as follows:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})=\frac{1}{5}\times-1=-0.2[/tex]

Thus, the value of [tex]\bar d[/tex] is -0.2.

Compute the value of [tex]s_{\bar d}[/tex] as follows:

[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}=\sqrt{\frac{0.48}{4}}=0.3464[/tex]

Thus, the value of [tex]s_{\bar d}[/tex] is 0.3464.

The variable [tex]\mu_{d}[/tex] represents the mean difference in body temperatures  measured at 8 AM and again at 12 AM.

Answer: there were 40 questions on her math final.

Step-by-step explanation:

Let x represent the total number of questions in the math test.

Mary got 85% correct on her math test. This means that the number of questions that she got right is

85/100 × x = 0.85 × x = 0.85x

This also means that the number of questions that she missed would be

x - 0.85x = 0.15x

Therefore, if Mary missed 6 questions, it means that

0.15x = 6

Dividing both sides of the equation by 0.15, it becomes

0.15x/0.15 = 6/0.15

x = 40

Step-by-step explanation:

Let x be line xy.

y represents line zm.

z is line zx or line zy

The area of one of the smaller triangles is x/2* y.

same for the other triangle.

The perimeter for either one of the triangles is x/2+y+z.

Answer:

5

Step-by-step explanation:

numerator degrees of freedom=[tex]Treatments-1[/tex]

[tex]N_d_f=5-1=4[/tex]

Total degrees of freedom=[tex]Treatments\times \ Observations Recorded-1[/tex]

[tex]T_d_f=5\times13-1=64[/tex]

Denominator Degrees of freedom=[tex]T_d_f-N_d_f=64-4=60[/tex]

Therefore, to calculate the degrees of freedom corressponding to treatments:

[tex]F=\frac{MSR}{MSE}\\MSR=200\div4=50\\MSE=(800-200)\div 60=10\\F=50\div10=5[/tex]

Answer:

the present value of the lease obligation for lease A will be $1,702,712.74 while the present value of lease B will be $1,764,741.73

Step-by-step explanation:

the present value of annual lease payment will be determined by discounting the total amount to be received from lease payment over years.

for lease A  , Pv =   A [tex]\fracA{1 -(1+r)^{-n} }{r}[/tex]

                         =   $200,000( 1 - (1+0.1)[tex]^{20}[/tex]) / 0.1 =  $1,702,712.74

for lease B , Pv =   $220,000( 1 - (1+0.1)[tex]^-{17}[/tex]) / 0.1  =  $1,764,741.73

the amount to be dicloased in the balance sheet at 31 december, 2018

The present value of lease payments assesses the current value of future lease liabilities, using a specified interest rate. Calculations for Lease A and Lease B would involve discounting their respective future lease payments at the given 10% interest rate to understand the company's financial obligations.

Present Value of Lease Payments

The present value of lease payments is a critical financial measure used by companies to assess the value of lease liabilities on their balance sheets. Generally, it accounts for all lease payments, discounted by a specific interest rate that reflects the time value of money. For Lease A, the company will make 20 annual payments of $200,000 each, starting on January 1, 2019. For Lease B, the company will make 17 annual payments of $220,000 each, starting on January 1, 2022. Using a discount rate of 10%, the present value of these lease payments can be calculated using the formula for the present value of an annuity.

For example, if a firm borrows $10,000 at an annual interest rate of 10%, it will owe $11,000 after one year because the original amount will accumulate interest. This illustrates the principle that a dollar today is worth more than a dollar in the future due to its potential to earn interest. Accordingly, the present value calculations for Lease A and Lease B will provide the amount the company should theoretically be willing to pay today to cover the lease payments over the course of the respective lease terms.

Answer:

0.1577 or 15.77%

Step-by-step explanation:

The Poisson probability model follows the given relationship:

[tex]P(X=k) =\frac{\lambda^k*e^{-\lambda}}{k!}[/tex]

For a Poisson model with a parameter λ = 3.85 Punch Baggies/hour, the probability of X=2 successes (exactly 2 Punch Baggies in an hour) is given by:

[tex]P(X=2) =\frac{3.85^2*e^{-3.85}}{2!}\\P(X=2) =0.1577=15.77\%[/tex]

The probability is 0.1577 or 15.77%.

Answer: The slope of the tangent line at density 200 is -1.67kg/bean stem

Step-by-step explanation: The attached graph file shows the relationship between the yield of a certain crop f(×) as a function of the density of aphid x.

The second attached file shows the solution.

Answer: $553.20

Step by step explanation: Since they took the price down 29% multiply the price by 1.29 to add the 29 percent back to the total amount. 428.84 * 1.29 = 553.20