two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below:
n1=37, ¯x1=53.5, s1=5.8n2=40, ¯x2=71.3, s2=10.3
Find a 94%94% confidence interval for the difference μ1−μ2 of the means, assuming equal population variances.

Answer:

Step-by-step explanation:

Split the quadrilateral into 2 triangles as pictured

One of them is right triangle with 2 sides known

The third side is the hypotenuse and is:

Total area is the sum of the areas of the 2 triangles

Area 1

Use Heron's formula for the second triangle:

Total area

P(Odd or Less than 4) = P(Odd) + P(Less than 4) - P(Odd and Less than 4)= 1/10 + 3/52 - 0= 13/130= 1/10, which is the final answer.

The probability that you pick an odd or less than 4 from a card at random can be calculated using the formula for the addition rule of probability that states that the probability of either of two events happening is the sum of their individual probabilities. In this case, the two events are picking an odd card and picking a card less than 4.Picking an odd card:

There are 5 odd cards in a deck of 52 playing cards, namely, Ace of hearts, 3 of hearts, 5 of hearts, 7 of hearts, and 9 of hearts. Thus the probability of picking an odd card from a deck of 52 playing cards is given by:P(Odd) = 5/52 = 5/52Reducing the above fraction to its simplest form by dividing the numerator and denominator by their greatest common factor, we obtain:

P(Odd) = 5/52 = 1/10Picking a card less than 4:There are 3 cards less than 4 in a deck of 52 playing cards, namely, Ace of hearts, 2 of hearts, and 3 of hearts.

Thus the probability of picking a card less than 4 from a deck of 52 playing cards is given by:P(Less than 4) = 3/52Reducing the above fraction to its simplest form by dividing the numerator and denominator by their greatest common factor, we obtain:P(Less than 4) = 3/52

Therefore, the probability of picking either an odd card or a card less than 4 from a deck of 52 playing cards is given by:P(Odd or Less than 4) = P(Odd) + P(Less than 4) - P(Odd and Less than 4)Where P(Odd and Less than 4) is the probability of picking a card that is both odd and less than 4.

Since there are no cards in the deck that satisfy this condition, P(Odd and Less than 4) is equal to 0.

Hence:P(Odd or Less than 4) = P(Odd) + P(Less than 4) - P(Odd and Less than 4)= 1/10 + 3/52 - 0= 13/130= 1/10, which is the final answer.

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Answer:

Your answer should be A

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)

\( \tt \: 23 + 45 - \sqrt { 100 }\)

Add 23 and 45 to get 68.

\( \tt \: 68-\sqrt{100} \)

Calculate the square root of 100 to get 10.

\( \tt \: 68-10 \)

Subtract 10 from 68 to get 58.

\( = \boxed{\boxed{ \bf \: 58}}\)

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}} \implies \cfrac{-14}{3 +4}\implies \cfrac{-14}{7}\implies -2\)

Answer:

(25 x 3) - 14 = 61!

Step-by-step explanation:

The number of liters it would take to fill this box would be 1 liter .

The number of liters that would go into the box can be found by finding the volume of the box as liters are a measure of volume .

To find the volume of the box, multiply its dimensions :

Volume = width × length × height

Volume = 20 cm × 10 cm × 5 cm

Volume = 1, 000 cm³

Since 1 liter is equal to 1000 cm³, the box can fit 1 liter of liquid .

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Use the slope formula below:

\( \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }\)

The m-term represents the slope.

The formula is the changes of two y-points over the changes of two x-points. We are given two points. Substitute both points in the formula.

\( \large{m = \frac{9 - ( - 7)}{ - 2 - 4} } \\ \large{m = \frac{9 + 7}{ - 6} \longrightarrow \frac{16}{ - 6} } \\ \large{m = \frac{8}{ -3 } \longrightarrow - \frac{8}{3} }\)

Therefore the slope is -8/3

Answer

Hope this helps! Let me know if you have any doubts.

Answer:

y = -8 / 3x + 11/3

Step-by-step explanation:

Using the slope formula:

\(slope = y = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\)

1. Select one point to be \((x_{1} ,y_{1} )\) and the other \((x_{2} ,y_{2} )\)

I chose (-2, 9) to be \((x_{1} ,y_{1} )\) and (4, -7) to be \((x_{2} ,y_{2} )\)

2. Plug the values into the formula:

\(y = \frac{-7-9}{4-(-2)} \\\\y= \frac{-16}{6} \\\\y = \frac{-8}{3}\)

3. Finding the c-value by plugging in one of the points into the equation

y = mx + c

9 = -8/3 (-2) + c

9 = 16/3 + c

c = 11/3

4. y = -8/3x + 11/3

3 apple + 7 blackberrys = 99

2 apple + 14 blackberrys = 178

Then now find

apples = (99 - 7 B)/3 = (178 - 14B)/2

Now make cross multiply

(99 - 7B) •2 = (178 - 14B) •3

Solve parenthesis, use a (b+c) = ab + ac

Then

198 - 14B = 534 - 42B

Now find Blackberrys B PRICE

42B - 14B = 534 - 198

28B = 336

B= 336/28 = 12

Now find Apples price

Apples= ( 99 - 7B) /3 = (99 - 7•12)/3 = 15/3= 5

Then final answer is

Apple's price= $5

Blackberry's price= $12

Answer:

9/2

Step-by-step explanation:

To find the gradient of a line passing through two points, we can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Using the points (1, 4) and (-1, -5), we have:

m = (-5 - 4)/(-1 - 1)

= (-9)/(-2)

= 9/2

Therefore, the gradient of line L is 9/2.

\(1.25\)

\(3 \times \frac{5}{8} - 2 \times \frac{3}{8} = \frac{29}{8} - \frac{19}{8} = \frac{10}{8} = 1.25\)

A) The nth number of the sequence can be calculated recursively using the given recurrence relation: y_n = 7y_{n-1} + 12y_{n-2}.

To find the nth number of the sequence, we can use the given recurrence relation. Let's denote the nth number as y_n.

Given that the first number is zero (y_1 = 0) and the second number is unity (y_2 = 1), we can start generating the sequence as follows:

n = 1: y_1 = 0

n = 2: y_2 = 1

For n ≥ 3, the nth number is the sum of seven times the (n-1)th number and twelve times the (n-2)th number:

y_n = 7y_{n-1} + 12y_{n-2}

Using this recurrence relation, we can calculate the sequence as follows:

n = 3: y_3 = 7y_2 + 12y_1 = 7(1) + 12(0) = 7

n = 4: y_4 = 7y_3 + 12y_2 = 7(7) + 12(1) = 61

n = 5: y_5 = 7y_4 + 12y_3 = 7(61) + 12(7) = 469

and so on...

Therefore, the nth number of the sequence can be calculated recursively using the given recurrence relation: y_n = 7y_{n-1} + 12y_{n-2}.

B) The general solution is the sum of the particular solution and the complementary solution:

y_n = A(3^n) + B(-2^n) + (-3/4)n - 5/6

To solve the difference equation y_{n+2} - y_{n+1} - 6y_n = 3n + 5 using the undetermined coefficient method, we assume that the solution can be expressed as a linear combination of terms involving the right-hand side of the equation.

Let's assume that the particular solution is of the form:

y_n = An + B

Substituting this into the difference equation, we have:

(A(n+2) + B) - (A(n+1) + B) - 6(An + B) = 3n + 5

Simplifying, we get:

An + 2A + B - An - A - B - 6An - 6B = 3n + 5

Combining like terms, we have:

-4An - 6B = 3n + 5

For the equation to hold for all values of n, the coefficients of the corresponding terms on both sides must be equal:

-4A = 3 (coefficient of n on the right-hand side)

-6B = 5 (constant term on the right-hand side)

Solving these equations, we find A = -3/4 and B = -5/6.

Therefore, the particular solution is:

y_n = (-3/4)n - 5/6

To obtain the general solution, we need to find the complementary solution to the homogeneous equation y_{n+2} - y_{n+1} - 6y_n = 0. This can be done by assuming a solution of the form y_n = r^n, where r is a constant.

Solving the characteristic equation r^2 - r - 6 = 0, we find two roots r1 = 3 and r2 = -2.

Hence, the complementary solution is:

y_n = A(3^n) + B(-2^n)

Therefore, the general solution is the sum of the particular solution and the complementary solution:

y_n = A(3^n) + B(-2^n) + (-3/4)n - 5/6

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It's 16.

The difference between two consecutive numbers is one more than between the previous two numbers.

1+1=2+2=4+3=7+4=11+5=16+6=22

There are the steps you can take to complete the frequency table, construct a histogram, and construct a pie chart using the data provided in the table below:

| Score | Frequency |
|-------|-----------|
| 40-49 |     2     |
| 50-59 |     3     |
| 60-69 |     5     |
| 70-79 |     6     |
| 80-89 |     4     |

a. To complete the frequency table for the math test scores, simply count the number of scores that fall within each range (e.g. 40-49, 50-59, etc.). You can see that there are 2 scores between 40 and 49, 3 scores between 50 and 59, 5 scores between 60 and 69, 6 scores between 70 and 79, and 4 scores between 80 and 89.

b. To construct a histogram of the data, you will need to plot the frequency of each score range on a graph. The x-axis should show the score ranges (e.g. 40-49, 50-59, etc.) and the y-axis should show the frequency. Each bar on the histogram will represent a score range and its height will represent the frequency. Here is what the histogram would look like for this data:

```
8 |
  |
7 |
  |
6 |           ******
  |         *********
5 |       ***********
  |      ************
4 |     **************
  |    ****************
3 |  ******************
  | *******************
2 |********************
  --------------------
    40-49 50-59 60-69 70-79 80-89
```

c. To construct a pie chart of the data, you will need to calculate the percentage of scores that fall within each range. To do this, add up the frequencies for all the score ranges and divide each frequency by this total. Then, multiply by 100 to get the percentage. Here are the percentages for this data:

- 40-49: 10%
- 50-59: 15%
- 60-69: 25%
- 70-79: 30%
- 80-89: 20%

To create the pie chart, draw a circle and divide it into 5 sections, one for each score range. Each section should be labeled with the score range and its percentage. The size of each section should be proportional to its percentage. Here is what the pie chart would look like for this data:

```
       40-49 (10%)
        -----
      /       \
    /           \
50-59 (15%)   70-79 (30%)
    \           /
      \       /
        -----
       60-69 (25%)

           |
           |
       80-89 (20%)
```

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Answer:

You need to give more information.

Step-by-step explanation:

Answer:

25% is 0.25

0.08 is 8%

Step-by-step explanation:

Percent is how much per 100, so 25% means 25/100.

0.08 means 8/100, which is 0.08 which is 8%

Answer:1. 0.25

2. 8%

A percent is a decimal multiplied by 100 and vice versa

Answer:

310 miles

Step-by-step explanation:

You can set up a proportion and solve for x.

2 6.2

___ = ___

100 x

Cross multiply

2x=6.2*100

Simplify

2x=620

Divide each side by 2

x=310

Answer:

D. 60cm²

Step-by-step explanation:

First, notice how the partially shaded squares fit perfectly into one another (the squares are perfectly cut from corner to corner). Once you match these squares to one another, you can then figure out that they add up to three full squares.

Secondly, measure how many squares there will be in the diagram after adding up the partial squares (resulting in a total of 15).

Finally, calculate the area of one of the squares (2cm x 2cm), which results in 4cm². As you have 15 total squares, multiply 4cm² by that to get the final answer of 60cm².

Given:

Tommy earned $14.80 in interest after 4 years on a principal of $100. His simple interest rate is 3.7%

Jane earned $140.40 in interest after 3 years on a principal of $1,200. Her simple 3 interest rate is 3.9%.

So, the simple interest rate of Jane's is greater than the simple interest rate of Tommy's because 3.9% > 3.7%

so, the bank that would be used is Jane's bank

a. The probability that the project will be finished in 40 weeks or less can be determined using the normal distribution and the concept of Z-scores.

First, we need to calculate the standard deviation (σ) of the critical path duration, which is the square root of the variance (σ^2). In this case, the variance is given as 9, so the standard deviation is √9 = 3. Next, we calculate the Z-score for the desired completion time of 40 weeks. The Z-score is calculated by subtracting the expected completion time from the desired completion time and dividing it by the standard deviation: (40 - 40) / 3 = 0. Using a standard normal distribution table or a calculator, we can find the probability associated with the Z-score of 0. In this case, the probability is 0.5000. Therefore, there is a 50% probability that the project will be finished in 40 weeks or less.

b. The probability that the project takes longer than 40 weeks can also be determined using the normal distribution. Since we already know the Z-score for 40 weeks is 0, we can calculate the probability of the project taking longer by finding the area under the normal distribution curve to the right of the Z-score of 0. The area to the right of 0 represents the probability of the project taking longer than 40 weeks. By looking up the Z-score of 0 in the standard normal distribution table or using a calculator, we find that the probability is 0.5000. Therefore, there is a 50% probability that the project will take longer than 40 weeks.

The probability of the project being finished in 40 weeks or less is 50%, while the probability of the project taking longer than 40 weeks is also 50%. These probabilities are based on the given variance of 9 and the assumption that the project duration follows a normal distribution.

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Answer:

x=10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x + 35 and MZ = 5x - 22. 146 136 156.

Answer:

9996

Step-by-step explanation:

Answer:

cost of football = 7.49

cost of tennis = 2.25

Step-by-step explanation:

Answer:

A. 525.42 inches^3

B. 175.91 mm

Step-by-step explanation:

a. Here we are asked to calculate the volume of the cone given the radius and the height of the cone.

Mathematically, the volume of the cone can be calculated using the formula below;

V = 1/3 * π * r^2 * h

where r is the radius which is 5.1 inches and h is the height of the megaphone = 19.3 inches

Plugging these values, we have;

V = 1/3 * 3.14 * 5.1^2 * 19.3 = 525.42 inches^3

b. Here we are tasked with calculating the height given the value of the volume and the radius.

mathematically, the formula to use is

V = 1/3 * π * r^2 * h

where V = 356,456.2136 cubic millimeter and r is 44mm

plugging these values we have

356,456.2136 = 1/3 * 3.14 * 44^2 * h

h =( 1,069,368.6408)/6,079.04

h = 175.91 mm

28. 0.16 (add a line above 6)

29. 0.45 (add a line above 45)

30. 0.4 (add a line above 4)

31. 0.27 (add a line above 7)

32. 0.037 (add a line above 037)

33. 0.045 (add a line above 45)

34. 0.27 (add a line above 27)

35. 0.148 (add a line above 148)

36. 0.16 (add a line above 6)

37. 2.83 (add a line above 3)

Why?

Just divide the 1st number by the last numberb and if the numbers repeat at the end, add a line above them!

Answer:

2955

Step-by-step explanation:

The ratio of yes votes to no votes is 3:2.

The total ratio is:

3 + 2 = 5

Let the total number of votes be x.

The number of yes votes was 1773. This means that:

3/5 * x = 1773

3x = 1773 * 5

x = (1773 * 5) / 3

x = 2955 votes.

There were 2955 votes in total.

Answer:

2, 4

Step-by-step explanation:

Answer: a and c are polynomials, b is not.

Step-by-step explanation:

A polynomial p(x) is written as:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰

where x is the variable, and the numbers aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, such that aₙ is the leading coefficient, and the value of n (always a natural number) is the degree of the polynomial.

Notice that the powers need to be always natural numbers.

Now, let's analyze the options:

a) 3*x - 2

We can rewrite this as:

3*x¹ - 2*x⁰

Then this is a polynomial.

b) p² + 1/p    (in this case the variable is p)

the second term can be written as:

1/p = p⁻¹

Then we have a term with a negative power of p, this means that this is not a polynomial.

c) 3*y² - 2*y/3 + 1

Same as in the first case, we can rewrite this as:

3*y² - (2/3)*y¹ + 1*y⁰

This is a polynomial.