The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?

Answer:

D

Step-by-step explanation:

You can plug in the given x and y values into the equations and see which one works for both of them.

D works for both of them:

5 = 5/4(4)

0 = 5/4(0)

Answer:

y=5/4x

Step-by-step explanation:

I just took the TSI2 and it says its correct

Answer:

A

A has sufficient sunlight, it's also close to some vegetation, it's the perfect place.

Answer:

It is Point B not Point A

Step-by-step explanation:

i have done the test a little bit ago.

Answer:

B 3(20-y-3)

Step-by-step explanation:

This is the answer u lookin for ✌

Answer:

Step-by-step explanation:

Answer:

the dimensions in the drawing are 16.25 inches by 6.375 inches

Step-by-step explanation:

The first thing is to use the same unit on the scale, that is, they tell us that the scale is 1:40 but that scale cannot be applied because they are different units of measurement.

The answer is preferable to give it in inches because it is more adapted to the measurements in a drawing, therefore we will pass the scale all in inches, knowing that 1 foot is 12 inches:

40 feet * 12 inches / 1 foot = 480 inches, therefore the scale is 1: 480

Now, if we pass the dimensions that give us inches, we are left with:

650 feet * 12 inches / 1 foot = 7800 inches

255 feet * 12 inches / 1 foot = 3060 inches

Now applying the scale:

7800/480 = 16.25

3060/480 = 6.375

It means that the dimensions in the drawing are 16.25 inches by 6.375 inches

Answer: A.

The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Explanation: a system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column. Since every column of the coefficient matrix is a pivot column, none of the leading coefficients are in the rightmost column of the augmented matrix. Therefore the rightmost column of the augmented matrix cannot be a pivot column and the system must be consistent.

Answer:

S) 230°

T) 45°

Step-by-step explanation:

S) m∠RST = 30°.  An inscribed angle is half the central angle, so RT = 60°.

SR = 70°, so ST = SR + RT = 60° + 70° = 130°.

SPT = 360° − ST = 360° − 130° = 230°

T) m∠DCA = 60°.  An inscribed angle is half the central angle, so AD = 120°.

DB = AD − BA = 120° − 75° = 45°

Answer:

  104 inches

Step-by-step explanation:

No window dimensions are given. We might assume that the shape of the window can be defined by these coordinates:

   (18,64), (28,40), (18,16), (8,40)

A graph of the points reveals the window to be a rhombus, so we can figure the length of one side to determine the lengths of all sides.

On edge of the window will have a length determined by the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

For (x1, y1) and (x2, y2) as (8, 40) and (18, 64), the edge length is ...

  d = √((18 -8)^2 +(64 -40)^2) = √(10^2 +24^2) = √676

  d = 26 . . . . . the length of one of the four edges

The total length of the four window edges is ...

  4 × 26 = 104

104 inches of tape are needed.

Answer:

The mean absolute deviation (MAD) of the dataset is 33.333.

Step-by-step explanation:

The mean absolute deviation (MAD) of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

These are the steps to calculate the mean absolute deviation.

Step 1: Calculate the mean.

[tex]Mean = \frac{20+90+25+100+85+30}{6} =\frac{175}{3}\approx58.333[/tex]

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

[tex]|20-\frac{175}{3} |=\frac{115}{3}\\\\|90-\frac{175}{3} |=\frac{95}{3}\\\\|25-\frac{175}{3} |=\frac{100}{3}\\\\|100-\frac{175}{3} |=\frac{125}{3}\\\\|85-\frac{175}{3} |=\frac{80}{3}\\\\|30-\frac{175}{3} |=\frac{85}{3}[/tex]

Step 3: Add those deviations together.

[tex]\frac{115}{3}+\frac{95}{3}+\frac{100}{3}+\frac{125}{3}+\frac{80}{3}+\frac{85}{3}=\frac{600}{3}=200[/tex]

Step 4: Divide the sum by the number of data points.

[tex]MAD=\frac{200}{6} =33.333[/tex]

Answer:

work is shown and pictured

Answer:

y=7/3

Step-by-step explanation:

Answer:

7/3 = y

Step-by-step explanation:

-5+8=-3y+10

3 = -3y + 10

Subtract 10  from each side

3- 10 = -3y +10-10

-7 = -3y

Divide each side by -3

-7/-3 = -3y/-3

7/3 = y

Answer:

$5.66/gal

Step-by-step explanation:

To calculate the current price of gas, multiply $4.35/gal by (1 + 0.30), or by 1.30:

1.30($4.35/gal) = $5.66/gal

Answer: Supplementary Angles

Step-by-step explanation:

∠5 and ∠6 are supplementary angles. If you look at their position, they are right next to each other. Both angles added together makes a straight line, which is 180°. Any 2 angles that make 180° are called supplementary angles.

Answer:

20

Step-by-step explanation:

When we use Pythagorean Theorem we get x² + 21² = 29² which means x = 20.

Answer:

B: 20

Step-by-step explanation:

By the pythagorean thereom, x^2+21^2=29^2. Solving gives X^2=29^2-21^2=400, so X=20.

Answer:

Step-by-step explanation:

When we propose an hypothesis, it is either true or false. The same goes for a proposition.

The required objective here is to determine the truth value in the following proposition.

(a) The integer 24 is prime.

(b) Is the integer 3​15​ even?

(c) The sum of 3 and 4 is 12.

(d) -4 ∈ Ζ

From the first option:

(a) The integer 24 is prime.

The sentence is a proposition but the truth value is FALSE because a prime number is a number that can only be divide by 1 and itself but in the case of 24, Its factors include  1,2,3,4,6,8,12 and 24 which make 24 to falsify the proposition of being  a prime number.

(b) Is the integer 3​15​ even?

This option is not a proposition but rather a question since it has a question mark, however, 315 is an odd number since it is not divisible by 2.

( c)  The sum of 3 and 4 is 12.

This is a proposition and the truth value is FALSE

The sum of 3+4 = 7  ; Hence; 7 ≠ 12

(d)   -4 ∈ Ζ

This is a proposition and the truth value is TRUE.

-4 ∈ Ζ  is read as ( minus four is an integer  (∈)  of Z )

Yes, this is a proposition and its Truth value is TRUE , since  minus four is an integer  (∈)  of Z

Answer:

1

Step-by-step explanation:

We can find the slope by using

m = (y2-y1)/(x2-x1)

    = (-2-2)/(-2 -2)

    =-4/-4

    =1

Answer:

Your answer would be 1

Step-by-step explanation:

Slope formula = y2-y1/x2-x1

x1y1=2,2 and x2y2=-2,-2

Plug the values in:

= -2-2/-2-2 = -4/-4 = 1

Answer:

 Japanese car

Step-by-step explanation:

Given

  problem details in Attachment 1

Find

  the most economical car

Solution

The attached spreadsheet shows the costs of repairs, insurance, and gas for each of the cars, using the cost factors described in the problem statement. (Numbers are displayed rounded to dollars.)

Mileage each year is assumed to be 150,000/8 = 18,750.

The "present value" line shows the present (year 0) value of the listed costs. The present value is the sum of values divided by 1.05^(year number). It is calculated using the spreadsheet NPV function.

The green total is the sum of present values to its right and the initial cost. The end value is subtracted after it is discounted by 1.05^8.

The Japanese car has the lowest present value.

___

The third attachment is the spreadsheet in Open Office format.

Answer:

a) A sample size of 5615 is needed.

b) 0.012

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99.5% confidence level

So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that [tex]\pi = 0.2[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}[/tex]

[tex]0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}[/tex]

[tex]\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}[/tex]

[tex]n = 5615[/tex]

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now [tex]\pi = 0.12, n = 5615[/tex].

We have to find M.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 2.81\sqrt{\frac{0.12*0.88}{5615}}[/tex]

[tex]M = 0.012[/tex]

Answer:

The value that will create an equation with no solutions is 5x.

Step-by-step explanation:

No solution would mean that there is no answer to the equation. It is impossible for the equation to be  true no matter what value we assign to the variable.

To create a no solution equation, we can need to create a mathematical statement that is always false.  To do this, we need the variables on both sides of the equation to cancel each other out and have the remaining  values to not be equal.

Use distributive property on the left side first.

[tex]3(x - 4) = [blank] - 2x +7\\\\3x-12=5x - 2x +7\\\\3x-12=3x+7\\\\3x-12+12=3x+7+12\\\\3x=3x+19\\\\3x-3x=3x+19-3x\\\\0=19[/tex]

Notice that we combined like terms first and then eliminated the variable from one side. When that  happened, the variable on the other side was eliminated as well, giving us a false result.

Since zero does not equal nineteen, we know we have an equation with no solution.

Answer:

Hospital A is less likely to record an average birth weight of at least 3400 g.

Step-by-step explanation:

Applying the Central Limit Theorem and the normal probability distribution.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Applying the Central Limit Theorem to find the z-score.

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

Probability of an average birth weight of at least 3400 g?

This probability is 1 subtracted by the pvalue of Z when X = 3400.

Mean is 3100, so [tex]\mu = 3100[/tex]

Suppose s is the same for both.

Hospital A:

n = 50. So

[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{50}}[/tex]

[tex]Z = \frac{300\sqrt{50}}{s}[/tex]

Hospital B:

n = 10. So

[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{10}}[/tex]

[tex]Z = \frac{300\sqrt{10}}{s}[/tex]

Comparasion:

[tex]\frac{300\sqrt{50}}{s} > \frac{300\sqrt{10}}{s}[/tex]

This means that hospital A has the higher z-score.

The higher the z-score, the higher the pvalue.

So, for A, 1 subtracted by the pvalue of Z when give a lower value than the 1 subtracted by the pvalue of Z in b. This means that hospital A is less likely to record an average birth weight of at least 3400 g.

Answer:

3

Step-by-step explanation:

2*1+1

2+1

3

how this helps :)

Answer: The clubs goal is to raise  $436.

Step-by-step explanation:

175%  * x  = 763     where x is the goal  

1.75 *x  = 763

1.75x = 763

x= 436

[tex]\$436[/tex]

A percentage is a number or ratio expressed as a fraction of [tex]\boldsymbol{100}[/tex]

Percentage of amount raised for charity [tex]=175\%[/tex]

Amount raised for charity [tex]=\$763[/tex]

Therefore,

[tex]175\%[/tex] of amount of goal [tex]=\$763[/tex]

    [tex]\frac{175}{100}\times [/tex] Amount of goal  [tex]=\$763[/tex]

Amount of goal [tex]=\frac{76300}{175} [/tex]

                          [tex]=\boldsymbol{\$436}[/tex]

For more information:

https://brainly.com/question/2724587?referrer=searchResults

Answer:

Step-by-step explanation:

Hello!

The random sample of n= 16 participants was asked to taste test two different sodas cans and rate them on a scale from 1 to 10. The cans contained the same type of soda but differ in color.

Since each participant tasted and ranked the two types of soda cans, you have per person a pair of data (X₁;X₂):

Where

X₁: Rank given to the red soda.

X₂: Rank given to the blue soda.

As said, the data is arranged in pairs per experimental unit, so these two variables are dependent, to study them is best to determine a third variable, the difference between X₁ and X₂:

Xd: X₁ - X₂

Assuming Xd~N(μd;σd²)

The objective is to test if there is any difference between the ratings based on the can color. The statistic hypotheses are:

H₀: μd=0

H₁: μd≠0

To calculate the descriptive statistics you have to calculate first the difference of each pair of ratings (see table in attachment)

Mean:

X[bar]d= ∑Xd/n= -6/16= -0.38

Variance

[tex]S_d^2=\frac{1}{n-1} [sumX_d^2-\frac{(sumXd)^2}{n} ]= \frac{1}{15}[64-\frac{(-6)}{^16} ]= 4.12[/tex]

Standard deviation

Sd= √4.12= 2.03

Statistic [tex]t= \frac{X[bar]_d-Mu_d}{\frac{Sd}{\sqrt{n} } } ~~t_{n-1}[/tex]

Df: n-1= 16-10 15

[tex]t_{H_0}= \frac{-0.38-0}{\frac{2.03}{4} } = -0.74[/tex]

P-value:

P(t₁₅≤-0.74) + P(t₁₅≥0.74)= P(t₁₅≤-0.74) + (1 - P(t₁₅≤0.74))= 0.2354 + (1 - 0.7646)= 0.4708

The decision rule for the p-value approach is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

α: 0.05

The p-value is greater than the level of significance, the decision is to not reject the null hypothesis.

At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that there is no difference between the rankings of the red and blue cans. I.e. there is no evidence to suggest that the can color changes the average ranting of the soda.

I hope this helps!

Answer:

[tex]216\sqrt{3}[/tex] [tex]cm^{2}[/tex]

Step-by-step explanation:

Length of edge:

[tex]12[/tex]

Length of apothem:

[tex]\frac{\sqrt{3}}{2}*12[/tex]

[tex]6\sqrt{3}[/tex]

3 × Length of edge × Length of apothem:

[tex]3*12*6\sqrt{3}[/tex]

[tex]216\sqrt{3}[/tex]

The answer is 96√3 cm²

Answer:

Thirty Residents Who Live Within a 2-Miles Radius Of Natasha’s School

Step-by-step explanation:

Answer:

The correct answer is "thirty residents who live within a 2-miles radius of Natasha’s school." or (D)

Step-by-step explanation:

teehee

Answer:

[tex]Area = 140[/tex]

Step-by-step explanation:

Given

R(6, 10)

Q(-9, 5)

S(2, -10)

Required

Area of triangle RQS

The are of RQS is calculated using the following formula;

[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]

Where x and y represent the axis of the given coordinates;

Given that R(6, 10);

[tex]R_x = 6 ; R_y = 10[/tex]

Given that Q(-9, 5);

[tex]Q_x = -9 ; Q_y = 5[/tex]

Given that S(2, -10);

[tex]S_x = 2 ; S_y = -10[/tex]

By Substituting these values in the given formula;

[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]

[tex]Area = \frac{1}{2} [6(-10 -5) + -9(10 - (-10)) + 2(5 - 10)][/tex]

[tex]Area = \frac{1}{2} [6(-15) + -9(10 + 10)) + 2(-5)][/tex]

[tex]Area = \frac{1}{2} [-90 + -9(20)) - 10][/tex]

[tex]Area = \frac{1}{2} [-90 -180 - 10][/tex]

[tex]Area = \frac{1}{2} [-280][/tex]

The expression |-280| means absolute value of -280 and the value is 280

[tex]Area = \frac{1}{2} [-280][/tex]

[tex]Area = \frac{1}{2}* 280[/tex]

[tex]Area = 140[/tex]

Hence, the area of the triangle is 140

Answer:

2 4/5

Step-by-step explanation:

5 4/5 - 2 3/3=2 4/5

Answer:

47/15 or 3 2/15

Step-by-step explanation:

first put it into improper fraction

so 29/5 minus 8/3

then find the least common denominator which is 15

87/15 minus 40/15 which is 47/15

simplify it

Answer:

Scores of students:

Mean: 34.3

Mode: no mode

No. of students:

Mean: 8.3

Mode: no mode

Step-by-step explanation:

(for scores of students)

6, 30, 35, 40, 45, 50

Mean: 6 + 30 + 35 + 40 + 45 + 50 = 206/6 = 34.3

Mode: there are no mode in the set of data.

(for No. of students)

4, 5, 6, 8, 12, 15

Mean: 4 + 5 + 6 + 8 + 12 + 15 = 50/6 = 8.3

Mode: no mode

Answer: y=-4/3x+22/3

Step-by-step explanation:

the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line

y=-4/3x+b

if you put in the x and y values

18=-4/3*-8+b

18-32/3=b

b=22/3

y=-4/3x+22/3

Answer:

x=2 or x=-2

Step-by-step explanation:

x2−4=0

Step 1: Add 4 to both sides.

x2−4+4=0+4

x2=4

Step 2: Take square root.

x=±√4

x=2 or x=−2