let y1 and y2 are independent random variables that are both uniformly distributed on the interval (0,1). find p(y1 <1

Answer:

In order of operations

Step-by-step explanation:

==> \(\frac{2}{7} \cdot 53 \cdot {7}{2} \\53 \cdot \frac{2}{7} \cdot {7}{2} \\\)  
Commutative property of multiplication : With multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. \(a \cdot b \cdot c = b \cdot a\cdot c\)

==> \(53 \cdot 1\)  
Multiplicative Inverse : A number multiplied by its reciprocal equals

1 : \(\frac{a}{b}\cdot\frac{b}{a} = 1\)

==> 53

Multiplicative Identity: Multiplying a number by 1 leaves the number unchanged: \(a\cdot1 = a\)

Answer:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

Step-by-step explanation:

A left tailed test is a type of test usually taken from the alternative hypothesis that includes only one of either the less than or greater than options and not both.

A left tailed test corresponds with the less than option and in this case study, the left tailed test are:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

An equation showing how many of each nut this nut bread contains is Y = 2p + 4w + 2t.

An equation is a mathematical expression of equality between two variables or expressions.

Equations are shown using the equation mark, symbol, or sign (=).

The number of walnuts in the nut bread = 1/2

The number of pecan nuts = 2

The number of walnuts which is double of pecan nuts = 4 (2 x 2)

The number of other nuts = 2 since walnuts equal 1/2 of the nuts

The total number of nuts = 8 (2 pecan, 4 walnuts, and 2 others)

Let the number of nuts in the bread = Y

Let the number of walnuts, w = 4

Let the number of pecan nuts, p = 2

Let the number of other nuts, t = 2 (8 - 4 - 2)

Thus, the equation of each nut contained in the nut bread is Y = 2p + 4w + 2t.

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The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.

Based on the information, the correct answer is B. Reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the age bracket is independent of the choice for the cause of the United States' involvement in other countries' nuclear programs.

The test statistic is greater than the critical value, so we reject the null hypothesis. This means that there is sufficient evidence to conclude that the age bracket is not independent of the choice for the cause of the United States' involvement in other countries' nuclear programs.

In other words, the age bracket of a respondent is related to the reason they believe the United States should be involved in restrictions made on other countries' nuclear programs.

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The probability that a ball selected at random from the jar is number 1, rounded to two decimal places, is 0.17.

To find the probability of selecting ball number 1 from a jar containing 6 balls numbered from 1 to 6, we need to determine the number of favorable outcomes (selecting ball number 1) and the total number of possible outcomes.

The total number of possible outcomes is 6 since there are 6 balls in the jar.

The number of favorable outcomes is 1 since we are interested in selecting ball number 1.

Therefore, the probability of selecting ball number 1 is given by:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 1 / 6

To express this probability in decimal form, we divide 1 by 6:

Probability ≈ 0.1666667

Rounded to two decimal places, the probability of selecting ball number 1 is approximately 0.17.

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Answer:

3 types of polynomials. They are monomial, binomial and trinomial.

-------------->

There can be rational, irrational and imaginary solutions. Irrational and imaginary solutions will always come in pairs. This is due to the fact that to find these types of solutions, you must use the Quadratic Formula and the \begin{align*}\pm\end{align*} sign will give two solutions.

Step-by-step explanation:

Answer:

See below ....question is a bit unclear

Step-by-step explanation:

He makes  133.33 per hour with shocks and only 100 per hour with brakes.

he should only do 36/3 = 12 shock jobs per week and no brakes.

  if he HAS to do at LEAST 3 brake jobs

     then he should do   3 brakes  and 10 shocks  

The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Answer: 27

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

G(2)= 2^2 +4(2)

Solve via order of operations

G(2)=4 +8

G(2)=12

The margin of error for 16 eggs with sample means 2 ounce and standard deviation as 42 ounces is   18.407   .

In the question ,

it is given that ,

the number of eggs = 16

the sample means weight is = 2 ounce .

the standard deviation is = 42 ounces .

we have to find the margin of error .

degree of freedom is 16 - 1 = 15 .

and the t score for the 90% confidence interval is

t₁₅,₀.₀₅ = 1.753

So , the margin of error is =  t₁₅,₀.₀₅×(standard deviation/√n)

Substituting the values ,

we get ,

= 1.753×(42/√16)

On simplifying further ,

we get ,

= 18.407

Therefore , the margin of error is = 18.407 .

The given question is incomplete , the complete question is

A sample of 16 eggs yields a sample mean weight of 2.00 ounces and a sample standard deviation = 42.0 ounces, find the margin of error in estimating a confidence interval estimate at the 90% level of confidence. Round your answer to three decimal places. You may assume that egg weights are normally distributed .

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Answer:

A small learning center holds 48 students

Step-by-step explanation:

A small Learning Center holds twenty-four less students than a large Learning Center. Together the Learning Centers hold seventy-two students. How many students does each Learning Center hold?

72-24=48

Step 1: Write out the definition of the function

Step 2: Find h(4)

h(4) is the value of h when x = 4.

Therefore,

Therefore,

h(4) = 1

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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Answer:

Area = 1

Step-by-step explanation:

I;ve attached my work below

Hope it helps, Let me know if you have any questions/concerns !

Have a nice rest of your day :)

Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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Answer:

The answer is 19.

Step-by-step explanation:

Because the 10 is 6 more than the 4, we subtract 6 from 25 (because they said that they were similar).

9514 1404 393

Answer:

  40°

Step-by-step explanation:

Since DP is an angle bisector, the angles it creates are congruent:

  ∠1 = ∠2 = 20°

The requested angle is the sum of the measures of angles 1 and 2:

  ∠FDE = ∠1 + ∠2 = 20° +20°

  ∠FDE = 40°

Answer:

The tank will empty in 4 hours.

Step-by-step explanation:

Since a barrel contains 56 liters of kerosene, and it has two taps, one tap that draws 500 ml every 6 minutes and after first 5 liters are drawn from the barrel, the second tap also starts, and it draws 1 liter in every 5 minutes, to determine how many hours will be taken in all to empty the tank, the following calculation must be performed:

0.5 x X = 5

X = 5 / 0.5

X = 10

10 x 6 = 60

1 hour = 51 liters

1 hour 30 minutes = 51 - (1 x 6) - (0.5 x 5) = 42.5

2 hours = 42.5 - (1 x 6) - (0.5 x 5) = 34

2 hours 30 minutes = 34 - (1 x 6) - (0.5 x 5) = 25.5

3 hours = 25.5 - (1 x 6) - (0.5 x 5) = 17

3 hours 30 minutes = 17 - (1 x 6) - (0.5 x 5) = 8.5

4 hours = 8.5 - (1 x 6) - (0.5 x 5) = 0

Therefore, the tank will empty in 4 hours.

The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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The red dot on the graph is (2, -8)

Answer:

12.56m²

Step-by-step explanation:

So the formula for the circumference of a circle is π x diameter, so we just have to plug into our equation (we're using 3.14 as π):

3.14 x 4 = 12.56

So the circumference of your circle is 12.56 meters²

hope this helps:)

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149 freshmen students, 32 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alpha = 0.01 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choose the correct answer below. H_0: p = 0.20 H_a: p not equal to 0.20 H_0: p not equal to 0.20 H_a: p = 0.20 H_0: p = 0.20 H_a: p 0.20 If alpha = 0.05, find the rejection region for the test. Choose the correct answer below. z > 1.645 z > 1.96 z

Solution:

We would set up the null and alternative hypothesis. The correct options are

For null hypothesis,

p ≥ 0.2

For alternative hypothesis,

p < 0.2

This is a left tailed test.

Considering the population proportion, probability of success, p = 0.2

q = probability of failure = 1 - p

q = 1 - 0.2 = 0.8

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 32

n = number of samples = 149

P = 32/149 = 0.21

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.21 - 0.2)/√(0.2 × 0.8)/149 = 0.31

The calculated test statistic is 0.31 for the right tail and - 0.31 for the left tail

Since α = 0.05, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.05/2 = 0.025

The z score for an area to the left of 0.025 is - 1.96

For the right, α/2 = 1 - 0.025 = 0.975

The z score for an area to the right of 0.975 is 1.96

In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96

Therefore, the rejection region is z > 1.96