A pair of dice was rolled. The random variable X represent the sum of the
numbers on the two dice. What is the probability mass function? What is the
cumulative mass function? Draw the probability mass function and the
cumulative mass function. What is the probability of getting an even value?
What is the probability that for a single roll of the two dice, the sum of the dots
is equal to 11? What is the probability of obtaining a value of 6 or less?

The value of x for the intersecting secants is derived to be equal to 10.7 to the nearest tenth.

The intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

(x - 3)(x + 1) = 6 × 15

x² + x - 3x - 3 = 90

x² - 2x - 93 = 0

using the quadratic formula;

x = 10.7 or x = -8.7

The segments must be positive so we take x = 10.7 so that;

x + 1 = 11.7

x - 3 = 7.7

Therefore, the value of x for the intersecting secants is derived to be equal to 10.7 to the nearest tenth.

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Answer:

65 feet

Step-by-step explanation:

Let x be the length of the expansion to the north, and y be the width of the expansion to the east.

The current patio has an area of 30 * 30 = 900 square feet.

The total area of the expanded patio will be 2500 square feet.

So, we need to find values of x and y that satisfy the following two conditions:

The area of the expanded patio is 2500 square feet:

xy = 2500

The expanded patio has walls on two sides, so it can only expand to the north and east:

x + 30 = y

We can solve the second equation for x:

x = y - 30

Substitute this expression for x in the first equation:

(y - 30)y = 2500

Simplifying this equation:

y^2 - 30y - 2500 = 0

We can solve for y using the quadratic formula:

y = (30 ± sqrt(30^2 + 4*2500)) / 2

y = (30 ± sqrt(10000)) / 2

y = (30 ± 100) / 2

Since y must be positive, we can ignore the negative solution:

y = (30 + 100) / 2 = 65

Substitute this value for y in the equation x + 30 = y:

x + 30 = 65

x = 35

Therefore, the expansion to the north should be 35 feet, and the expansion to the east should be 65 feet.

When there are large differences between robust standard errors and usual standard errors, we can conclude that there may be issues with the assumptions of the statistical model.

Robust standard errors are typically used when there are concerns about heteroscedasticity or the presence of outliers in the data. In contrast, usual standard errors assume that the errors are homoscedastic and normally distributed.

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Answer:

To determine when Bus A and Bus B will leave the station at the same time, we need to find the least common multiple (LCM) of their time intervals.

The time intervals for Bus A and Bus B are:

Bus A leaves every 45 minutes (i.e. intervals of 45 minutes)

Bus B leaves every 60 minutes (i.e. intervals of 60 minutes)

To find the LCM of 45 and 60, we can first factor each number into its prime factors:

45 = 3 x 3 x 5

60 = 2 x 2 x 3 x 5

The LCM is the product of the highest power of each prime factor, so:

LCM(45, 60) = 2 x 2 x 3 x 3 x 5 = 180

Therefore, Bus A and Bus B will leave the station at the same time every 180 minutes, or every 3 hours.

Since the buses begin their routes at 7:30 am, we can add multiples of 3 hours to this time to find when Bus A and Bus B will leave together.

The first time after 7:30 am when Bus A and Bus B leave together is:

7:30 am + 3 hours = 10:30 am

So Bus A and Bus B will leave the station together at 10:30 am, and then every 3 hours after that.

Answer:

3/4

Step-by-step explanation:

there are 4 spots and it is on the the third of them

John will earn an annual interest of $500 on a beginning balance of $10,000 at a rate of 5% per year. After one year, the ending balance will be $10,500. John earned $160 in interest after leaving his initial deposit of $8,000 in the bank for first year with annual compounding at a 2% interest rate. His ending balance was $8,160. The table shows his ending balance for years 5-10.

We can use the formula for simple interest to calculate the annual interest earned by John on a balance of $10,000 at a rate of 5% per year

Annual interest = (Principal x Rate x Time) / 100

where Principal is the beginning balance, Rate is the interest rate, and Time is the duration of investment in years.

Substituting the given values, we get

Annual interest = (10000 x 5 x 1) / 100 = $500

Therefore, the annual interest earned by John on a balance of $10,000 at a rate of 5% per year is $500.

Ending balance after one year = Beginning balance + Annual interest = $10,000 + $500 = $10,500.

since the term of the annual CD is four years, and John will leave his money in the bank for four years, we can calculate the ending balance at the end of each year using the formula above.

For year 5

P = $8,160

r = 0.02

n = 1

t = 1

A = $8,160 (1 + 0.02/1)^(1x1) = $8,324.80

For year 6

P = $8,324.80

r = 0.02

n = 1

t = 1

A = $8,324.80 (1 + 0.02/1)^(1x1) = $8,492.78

For year 7

P = $8,492.78

r = 0.02

n = 1

t = 1

A = $8,492.78 (1 + 0.02/1)^(1x1) = $8,664.28

For year 8

P = $8,664.28

r = 0.02

n = 1

t = 1

A = $8,664.28 (1 + 0.02/1)^(1x1) = $8,839.44

For year 9

P = $8,839.44

r = 0.02

n = 1

t = 1

A = $8,839.44 (1 + 0.02/1)^(1x1) = $9,018.34

For year 10

P = $9,018.34

r = 0.02

n = 1

t = 1

A = $9,018.34 (1 + 0.02/1)^(1x1) = $9,201.05

Therefore, the table for years 5 through 10 would look like

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The total volume of Mountain Dew in this six-pack is approximately 212.058 cubic inches.

Assuming that each can in the six-pack of Mountain Dew is cylindrical in shape, we can use the formula for the volume of a cylinder to calculate the volume of each can, and then multiply that by the total number of cans in the pack.

The formula for the volume of a cylinder will be;

V = πr²h

where V is volume, r is radius (half the diameter), and h is height.

The radius of each can is 1.5 inches (half of 3 inches), and the height is 5 inches. So the volume of each can is;

V = π(1.5)²(5) = 35.343 cubic inches

To find the total volume of the six-pack, we need to multiply this by the number of cans;

Total volume = 35.343 cubic inches/can × 6 cans

= 212.058 cubic inches

Therefore, the total volume is  212.058 cubic inches.

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Answer:

50 degrees Fahrenheit

Step-by-step explanation:

add 15f to cancel -15f and add the 35f left which is 50f

True. it is also appropriate to compare two means at a time using multiple independent two-sample t-tests in the same situation.

While a one-way ANOVA is appropriate for comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, it is also appropriate to compare two means at a time using multiple independent two-sample t-tests in the same situation.

However, using multiple t-tests may increase the probability of making a Type I error, so it is important to adjust the significance level or use a method such as the Bonferroni correction to account for multiple comparisons.

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Table B lists all the different ways Harry can get to Hogwarts and back. See the attached tables.

One mus tnote that both tables detail all of the alternative routes Harry can take to and from Hogwarts, however Table B is the only one that lists all of the different modes of transportation.

Table B includes all of the potential scenarios in which Harry can use the Knight Bus, Flying Car, or Hogwarts Express to and from Hogwarts, including situations in which he uses the same form of transportation both times. Table A, on the other hand, simply covers transit combinations, not all conceivable outcomes. So it is correct to state that as a result, Table B is the right solution.

See attached tables.

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The equation of the least-squares regression line for predicting the etching rate from the room temperature is 1.77 + 0.23x.

The least squares method is a form of mathematical regression analysis used to determine the line of best fit for a set of data, providing a visual demonstration of the relationship between the data points.

The equation of the least-squares regression line for predicting the etching rate from the room temperature is:

= 6.6 - 0.231 × 20.9 = 1.7721

y = 1.77 + 0.23x.

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Answer:

(i) [tex]B^c =[/tex] {1, 4, 6, 8}

(ii) A - (B - C) =  {4, 6, 8}

(iii) A ∩ (B ∪ C) =  {2, 3, 5, 7}

Step-by-step explanation:

We have the following sets

Universal set U = {x ∈ N, x ≤ 8}
This would all the numbers from 1 to 8 inclusive
U = {1, 2, 3, 4, 5, 6, 7, 8}

Set A = {x : 1 < x² < 65}

This would be all the numbers from U such that the square of those numbers lies between 1 and 65

Thus
A = {2, 3, 4, 5, 6, 7 ,8}
We exclude 1 because 1² = 1 is not included in the set definition
Highest is 8 because 8² = 64 < 65 and also 8 is the highest element in the set U

B = (x ∈ N: x is a prime number less than 10}
B = {2, 3, 5, 7 } these being the prime numbers less than 10

C = {x: x³ + 1 = 0, x ∈N}
if x³ + 1 = 0 ==> x³ = -1 and there is only one value of x that satisfies this relationship and that is x = -1 since (-1)³ = -1 and (-1)³ + 1 = 0

Now that we have enumerated the elements of all 4 sets we can solve the questions

(i) [tex]B^c[/tex] is the complement of set B = set of all elements not in set B
This would be the set of all numbers from 1 through 8 that are not prime

[tex]B^c[/tex] ={x: x is not a prime number and ≤ 8}

  = {1, 4, 6, 8}

(ii) A - (B - C)

B - C is the set difference between B and C

It is the set of all elements in B that are not in C

Since B = {2, 3, 5, 7} and C = {-1} no element of B appears in C so
B - C = B = {2, 3, 5, 7}

A - (B - C) = A - B

{2, 3, 4, 5, 6, 7 ,8} - {2, 3, 5, 7} = {4, 6, 8}

(iii) A ∩ ( B ∪ C)

B ∪ C = {2, 3, 5, 7} ∪ {-1} = {-1, 2, 3, 5, 7}
A ∩ (B ∪ C) =  {2, 3, 4, 5, 6, 7 ,8} ∩  {-1, 2, 3, 5, 7}

= {2, 3, 5, 7}

= B

I hope I got it right :)

The median of middle data values is 57.

Hence option (B) is correct.

In the given table;

total number of digits = 20

Since 20 is even number

Therefore its median = 20/2  + 1

                                   = 11

So the 11th digit of table is 7

Which gives index 5

Now according to the defined key 5|7 = 57

Hence median = 57

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The correct option is D that is the value of se represents the standard error of the estimate, which is a measure of the variability of the errors in predicting the response variable (weights) from the predictor variable (heights) using the regression equation.

Specifically, se represents the standard deviation of the residuals, which are the differences between the observed values of the response variable and the values predicted by the regression equation. A smaller value of se indicates that the regression equation provides a better fit to the data and that the predictions of the response variable are more accurate.

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Step-by-step explanation:

Two walls are   8x 9   and two walls are 10 x 9

8x9 x2   + 10x9 x2 = 324 ft^2

The domain of sin^-1(x) and cos^-1(x) are different while the domain of sin(x) and cos(x) are the same is due to the inverse properties and the range of their respective functions.

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Answer & Step-by-step explanation:

a)

√√√3 + √12

= √√(3)^(1/2) + √(4 x 3)

= √√(√3)^2 + √(4 x √3)^2

= √(√3 + 2√3)

= √3(1 + 2)

= 3√3

Therefore, √√√3 + √12 can be expressed in the form of a√3, where a = 3.

b)

(i)

1 + √(3)

To rationalize the denominator, we multiply the numerator and denominator by √3:

= 1 + √(3) * √(3) / √(3)

= 1 + √(9) / √(3)

= 1 + 3√(3) / 3

= (3 + √(3)) / 3

Therefore, 1 + √(3) can be expressed in the form of b√3, where b = (3 + √3) / 3.

(ii)

(5)^(1/3)

To rationalize the denominator, we multiply the numerator and denominator by √(3):

= (5)^(1/3) * √(3) / √(3)

= (5√(3)) / √(27)

= (5√3) / (3√3)

= (5/3)√3

Therefore, (5)^(1/3) can be expressed in the form of c√3, where c = 5/3.

Examples of acceleration are given as follows:

A) A runner slows down after passing another runner.

B) A runner speeds up at the end of a race.

The concept of acceleration is that the acceleration is defined as the change in the speed divided by the change in time, that is:

Acceleration = Change in speed/Change in time.

Hence any instance involving slowing down or speeding up involve acceleration, as it is the case for options A and B.

For options C and D, they do not involve acceleration, as the constant speed means that the change in the speed is of zero, hence the acceleration is also of zero.

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Answer: The length of the side of the supply closet is 6 feet

Step-by-step explanation:

1. We can separate the box into 2 rectangles.

3 x 8 and 2 x y

3 x 8 = 24

2. The whole closet is 36

36 - 24 = 12

3. The area of the 2 x y rectangle is 12

12/2 = 6

So the length of the y side is 6 feet.

The values of A-B and B-A are 27 and 36.

We are given that;

WA=(x/x=3".n≤6,nEN)

B= (x/x=9",n≤ 4,n € N)

Now,

First, let’s write the sets A and B using roster notation, which means listing all the elements inside curly braces.

A = {x | x = 3n, n ≤ 6, n ∈ N} = {3, 6, 9, 12, 15, 18}

B = {x | x = 9n, n ≤ 4, n ∈ N} = {9, 18, 27, 36}

Now, let’s find A - B by removing the elements that are common to both sets from A.

A - B = {3, 6, 9, 12, 15, 18} - {9, 18, 27, 36} = {3, 6, 12, 15}

Similarly, let’s find B - A by removing the elements that are common to both sets from B.

B - A = {9, 18, 27, 36} - {3, 6, 9, 12, 15, 18} = {27, 36}

Therefore, by the equation the answer will be 27 and 36.

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To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.

However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.

1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]

2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]

3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]

4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.

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[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{ns^2}{4}\cot\left( \frac{180}{n} \right) ~~ \begin{cases} n=\stackrel{sides'}{number}\\ s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ n=9\\ s=4 \end{cases}\implies A=\cfrac{(9)(4)^2}{4}\cot\left( \frac{180}{9} \right) \\\\\\ A=36\cot(20^o)\implies A\approx 98.91~m^2[/tex]

Make sure your calculator is in Degree mode.

Step-by-step explanation:

Area = 1/2 apothem × perimeter

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )r = 4/ ( 2 sin(20)

Area = 1/2 apothem × perimeter A= 1/2 r cos(20) × N × S we need to find radius so s = 2rsin(180/90)4 = r ( 2 sin(20) )r = 4/ ( 2 sin(20)r = 5.847 approximate to 6

when we go back

A = 1/2( 6 × cos(180/n) )×9×4

A = 1/2( 6 × cos(180/n) )×9×4A = 1/2( 6 × cos(180/9) )×9×4

A = 1/2( 6 × cos(180/n) )×9×4A = 1/2( 6 × cos(180/9) )×9×4A = 101.486m2 app|ozximate to 102 m2

Answer:

infinite number of solutions

Step-by-step explanation:

y = 5x + 3 → (1)

2y = 10x + 6 → (2)

substitute y = 5x + 3 into (2)

2(5x + 3) = 10x + 6

10x + 6 = 10x + 6

since both sides are the same then any value of x will make the equation true.

This means there are an infinite number of solutions to the system

Answer:

Step-by-step explanation: there are infinite solutions

Answer:

Juan has completed 0.7 of his assignment, which means he has not completed 0.3 of his assignment. This can also be expressed as a fraction: 3/10. Therefore, Juan has not completed 3/10 of his assignment.

Step-by-step explanation:

As per the given data, there are 42 different ways a stock boy and a secretary can be selected.

Based on the given information, there are 7 stock boys and 6 secretaries at the company. To find out how many different ways a stock boy and a secretary can be selected.

To find the number of ways a stock boy and a secretary can be selected, we need to multiply the number of choices for each position.

There are 7 stock boys to choose from, and 6 secretaries to choose from.

Therefore, the total number of ways a stock boy and a secretary can be selected is:

7 x 6 = 42

Thus, there are 42 different ways a stock boy and a secretary can be selected.

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The measurement that is closest to the area of the given desk would be = 103.26ft²

To calculate the area of the desk is to determine both the area of a trapezium and a quarter circle and add up the areas derived.

The formula of the area of trapezium = ½(a+b)h

where;

a = 9.5ft

b = 9.5+6 = 15.5

h = 6ft

area =½(9.5+15.5 )×6

= 25/2×6

= 75ft²

The area of quarter circle = πr²/4

r = 6ft

area = 3.14×36/4

= 3.14× 9

= 28.26ft²

Therefore the area of the shape;

= 75+28.26 = 103.26ft²

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Answer:

Step-by-step explanation:

formula for equation is

y=mx+b

b= y-intercept, meaning when x is 0, y=b

b= -1

m is slope = rise/run or [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

(1,2) (2,5)

m=[tex]\frac{5-2}{2-1} = \frac{3}{1}[/tex]     I picked the last 2 points because positive numbers are easier

m=3

now put into formula

y=3x-1

Answer:

To find the odds in favor of Cody being first, we need to divide the probability of him winning (25%) by the probability of him not winning (75%).

Odds in favor of Cody winning = 25% / (100% - 25%) = 25% / 75%

Simplifying, we get:

Odds in favor of Cody winning = 1/3

Therefore, the odds in favor of Cody being first in the 50m backstroke are 1 to 2 (or 1:2).