what is the probability of not rolling a 3 on a six sided die​

Using integration by part, the value of the integration over the interval is given as [(4√3 π - π + 2ln(2) - 4)] / 6

In the given question, we have a function which is;

f(x) = √x tan⁻¹ √x dx over an interval of lower limit 1 and upper limit of 3

Applying integration by parts

[2/3x^3/2 arctan(√x) - ∫ x/3(x + 1) dx]^3_1

We can simplify this into;

[1/3(2x^3/2 arctan(√x) - x - 1 + ln |x + 1|)] ^3_1

Let's compute the boundaries

[(4√3 π - π + 2ln(2) - 4)] / 6

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Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3

Step-by-step explanation:

The range of the men's scores is 75-65 (highest-lowest), which is 10.

The range of the woman's scores is 80-69, which is 11.

The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.

Men's MAD:
The mean is [tex]\frac{65+68+70+72+73+75}{6}[/tex], which is 70.5.

Sigh.

Now, we find the difference of each term to the mean.

[tex]70.5-65= 5.5[/tex]

[tex]70.5-68=2.5[/tex]

[tex]70.5 - 70 = 0.5[/tex]

[tex]72-70.5=1.5[/tex]

[tex]73-70.5=2.5[/tex]

[tex]75-70.5=4.5[/tex]

wow. Now, we find the mean of these numbers.

[tex]\frac{5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5}{6}[/tex]= 17/6=2.8333333333 This is the MAD.

For the Women's, I'll speed over it.

The mean is 74.

The MAD is 3.

Answer:

Step-by-step explanation:

the sum of the internal angles of a regular or irregular pentagon is 540°, we remove the known angles and we will have the answer

540 - 110 - 110 - 120 - 120 =

80°

The probability of hitting the center target is 3.8%.

To find the probability of hitting the center target, we need to know the total area of the larger target and the area of the center target.

The area of the larger target is:

16 inches x 20 inches = 320 square inches

The area of the center target is:

4 inches x 3 inches = 12 square inches

So, the probability of hitting the center target is:

12 square inches / 320 square inches = 0.0375 or 3.75%

Rounded to the nearest tenth of a percent, the probability of hitting the center target is 3.8%.

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Answer:

-2x > 6, so x < -3

So A is correct.

The correct answer is D. No, events E and G are not necessarily disjoint. The mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.

The example provided in option D shows that events E and F are disjoint, events F and G are disjoint, but events E and G are not disjoint. This is because they share the element 2.

For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} .

Therefore, the mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.

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The minimum value of the function on the interval [2, 11] is -100,000,000,000.

The function f(x) = -10ˣ is a decreasing exponential function, which means that its value decreases as x increases.

f(x) = -10ˣ on the interval [2, 11]

The minimum value of the function will be at the endpoint of the interval, which is at x=11.

f(11) = -10¹¹

f(11)= -100,000,000,000

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Answer:

the probability of picking two white socks is 1/3, or approximately 0.333.

Step-by-step explanation:

When choosing the first sock, there are 10 socks in total, and 6 of them are white. Therefore, the chance of picking a white sock on the first try is 6/10 or 3/5.

When picking the second sock, there are only 9 socks left in the drawer, since we did not replace the first sock. Of the remaining socks, 5 are white (since we did not replace the first white sock) and 4 are black. Therefore, the probability of picking a white sock on the second try, given that we picked a white sock on the first try, is 5/9.

Answer:  1/3

Step-by-step explanation:6*5/2 is number of ways that work. This is 15. There are 10*8/2=45 total ways. 15/45=1/3.

Answer:

The answer to your question is $375

The selling price of the cell phone is $375.

Step-by-step explanation:

15% x 2500

100 = 375

I hope this helps and have a wonderful day!

Answer:

65 apples

Step-by-step explanation:

We Know

John has 8 boxes of apples.

Each box holds 10 apples.

If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?

Let's solve

5 boxes are full: 5 x 10 = 50 apples

3 boxes are half full = 3(1/2 · 10) = 15 apples

50 + 15 = 65 apples

So, John has 65 apples.

A coin is biased so that the probability a head comes up when it is flipped is 0.6. Therefore, we can expect to get 6 heads when a biased coin with a probability of 0.6 for heads is flipped 10 times.

To find the expected number of heads when a biased coin is flipped 10 times, we can use the formula:

Expected number of heads = Probability of getting a head × Number of times the coin is flipped

In this case, the probability of getting a head is 0.6 and the coin is flipped 10 times. So the expected number of heads is:
Expected number of heads = probability of getting a head x number of times flipped

Expected number of heads = 0.6 x 10

Expected number of heads = 6

Therefore, the expected number of heads when the coin is flipped 10 times is 6.

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Answer: C. k is equal to one fourth

Step-by-step explanation:

formula for parabola in vertex form

y= a(x-h)²+k     (h, k) is vertex here it is (0,0)

f(x)=ax²   another point we can plug in is (1,2)

2=a1

a= 2

so f(x)= 2x²

g(x)= f(kx)     plug in kx into f(x)

g(x) = 2(kx)²

g(x) =  2(k²)(x²)    plug in a point and find k (4,2)

2 = 2 k²4²

k²=1/16

k=1/4

C

To solve the equation 2y − 2.3 = 4.1  for y, we can use algebraic manipulation.

In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:

                                 2y - 2.3 = 4.1

                     +2.3                          +2.3

                                   2y = 6.4

Now, we divide both sides by 2 to isolate y:

                                 2y = 6.4

                            ÷2               ÷2

                                  y = 3.2

So, the solution to this equation is  y = 3.2

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We need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.

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- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.

- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.

- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.

The main answer to your question is "interchanging". To find the inverse of a function, we interchange the numbers in each ordered pair of the function. This means that we switch the x and y values of each point in the function.

For example, if we have a function f(x) = 2x + 3, the ordered pairs would be (1,5), (2,7), (3,9), etc. To find the inverse function, we would switch the x and y values of each point to get ordered pairs such as (5,1), (7,2), (9,3), etc.

The explanation for why we interchange the numbers is that the inverse function "undoes" the original function. If we apply the original function to a number, the inverse function will take us back to the original number. By switching the x and y values, we make sure that the inverse function will undo the original function.

In conclusion, to find the inverse of a function, we interchange the numbers in each ordered pair of the function. This ensures that the inverse function will undo the original function.
Hi! I'm happy to help you with your question.

Main answer: The inverse of a function can be found by interchanging the numbers in each ordered pair of the function.

Explanation: When finding the inverse of a function, you are essentially swapping the input and output values in each ordered pair (x, y) to create a new ordered pair (y, x). This process is called interchanging the numbers in the ordered pair.

Conclusion: To find the inverse of a function, you need to interchange the numbers in each ordered pair of the function, which essentially swaps the input and output values.

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Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Since the confidence interval does not contain 0, it supports the alternative hypothesis that commercial trucks have a higher proportion of violations than passenger cars.

a. Hypothesis Test:

Null Hypothesis: The proportion of passenger cars with only rear license plates is equal to or greater than the proportion of commercial trucks with only rear license plates.

Alternative Hypothesis: The proportion of commercial trucks with only rear license plates is greater than the proportion of passenger cars with only rear license plates.

Let p1 be the proportion of passenger cars with only rear license plates, and p2 be the proportion of commercial trucks with only rear license plates.

The test statistic for comparing two proportions is the z-test.

z = ((p1 - p2) - 0) / √(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of successes (only rear license plates) in the two samples, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

p1 = 227/2094 = 0.1084

p2 = 46/330 = 0.1394

p_hat = (227 + 46) / (2094 + 330) = 0.1116

n1 = 2094

n2 = 330

z = ((0.1084 - 0.1394) - 0) / √(0.1116 * (1 - 0.1116) * (1/2094 + 1/330))

= -1.68

The p-value for this one-tailed test is P(Z < -1.68) = 0.0475.

Conclusion: The data provides sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

b. Confidence Interval:

We can also construct a confidence interval to estimate the difference in proportions with a specified level of confidence.

A 90% confidence interval for the difference in proportions can be calculated as:

(p1 - p2) ± z√(p1(1-p1)/n1 + p2*(1-p2)/n2)

Plugging in the values, we get:

(p1 - p2) ± 1.645√(0.1084(1-0.1084)/2094 + 0.1394*(1-0.1394)/330)

= (-0.0499, 0.0094)

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Answer:

18.3

Step-by-step explanation:

In order to convert Fahrenheit to Celsius, you need to use the formula:

[tex]C=\frac{5}{9}(F-32)[/tex]

Since F = 65, we can plug it in:

[tex]C=\frac{5}{9}(65-32)[/tex]

[tex]C=\frac{5}{9}(33)[/tex]

[tex]C=\frac{165}{3}[/tex]

[tex]C=18.33333333333333333333333333[/tex]

Rounding to the nearest tenth, we get

[tex]C = 18.3[/tex]

Answer:

------------------------------

Use the formula for compound interest :

Where:

In this problem, we have:

Now, let's plug these values into the formula:

After 6 years, Lex will have approximately $1780.77 in his savings account.

The required coefficient on x² is 2, so the answer is 2. Option B is correct.

We can start by assuming that the quadratic function has the form:

y = ax² + bx + c

where a, b, and c are unknown coefficients to be determined. We can use the three given points on the graph to set up a system of three equations in three unknowns:

7 = a(1)² + b(1) + c

16 = a(2)² + b(2) + c

29 = a(3)² + b(3) + c

Simplifying each equation, we get:

a + b + c = 7

4a + 2b + c = 16

9a + 3b + c = 29

We can solve this system of equations using any method of our choice, such as elimination or substitution. One possible approach is to subtract equation 1 from equation 2 and equation 2 from equation 3, which gives:

a + b + c = 7

3a + b = 9

5a + b = 13

a = 2; b = 3; c = 2

Therefore, the equation for the quadratic function in standard form is:

y = 2x² + 3x + 2

The coefficient on x² is 2, so the answer is 2.

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In the given graph, the length of the segment "AB" is 6.32units.

We have to find length of segment "AB", which means we have to find the distance between the end-points "A" and "B",

From the graph, the end-points of the segment "AB" are :

A ⇒ (-2,4) and B ⇒ (4,2),

So, the length(distance) between these two points can be calculated by the formula : √((x₂-x₁)² + (y₂-y₁)²);

Considering (-2,4) as (x₁, y₁) and (4,2) as (x₂, y₂);

We get,

Length(distance) = √((4-(-2))² + (2-4)²);

Length = √(6² + (-2)²); = √(36 + 4);

Length = √40 ≈ 6.32 units.

Therefore, the length of the segment is 6.32 unis.

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The probability that the length of time between charges will be between 40 and 70 hours is 0.656.

To solve this problem, we need to standardize the values of 40 and 70 using the given mean and standard deviation, and then use the standard normal distribution table to find the probability.

Standardizing 40: z = (x - mu) / sigma z = (40- 50)/15 z = -2/3

Standardizing 70: z = (x-mu) / sigma z = (70- 50)/15 z 4/3

Now we look up the probabilities associated

with the standardized values -2/3 and 4/3 in the

standard normal distribution table.

Using the table, we find that the probability of z being less than -2/3 is 0.2525 and the probability of z being less than 4/3 is 0.9082.

So the probability of the length of time being between 40 and 70 hours can be found by subtracting the probability of z being less than -2/3 from the probability of z being less than 4/3:

P(40 < x <70) = P(-2/3 <z < 4/3) = P(z < 4/3) - P(z< -2/3)

P(40 < x < 70) = 0.9082-0.2525 P(40 < x <70) = 0.6557

Therefore, the probability that the length of time between charges will be between 40 and 70 hours is approximately 0.656, which is closest to option B.

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Any number above 108 will be an upper outlier. So, there is no upper outlier.

Therefore, there is 1 outlier.

Mean  :

For a given distribution, the mean can be calculated by dividing the sum of all quantities with the number of quantities. Sometimes it referred to as average.

Median:

The median of a given data distribution is calculated as follows:

1. First arrange all the given data in ascending order.

2. If the number of data items is odd, then the centre data represents the median.

3. If the number of data items is even, then two numbers are in the central data. The average of those two data items is a median.

Mode

In the given data, the element which occurs number of times is called the mode of the data.

Step 2/14

a.

Consider the stem and leaf plot given in the text book that represents the money spent on gas in the last week by the selected seniors.

Compute the frequency of the given stem-and-leaf plot by counting its leaves. There are 27 leaves in the given plot.

Therefore, a total 27 students were polled.

Step 3/14

b.

Add the data represented in the plot and divide it by the frequency to compute the mean.

The sum of all data points is as follows,

1662

So, the mean of the given data set will be,

1662/27

=$61.56

Step 4/14

c.

The frequency of the given data set is an odd number (27).

So, the median will be the 14th data point.

From the given data set, 14th data point is $ 64.

Therefore, the median of the given data is. $64

Step 5/14

d.

The Mode of a given data set is the most occurring item.

From the given stem and leaf plot, the leaf 3 corresponding to the stem 5 is the most occurring data point (5 times).

Therefore, the mode of the given data is. $53

Step 6/14

e.

The Range is the difference between the greatest number and the least number in the given data set.

The lowest data point is 17 $ and the greatest data point is 84 $

Therefore, the range of the given data will be,

Range = 84 -17

=$67

Step 7/14

f.

The lower quartile of the given data set will be the 7th data point.

Therefore, Q1 = $54

The second quartile of the given data set will be equal to the median.

Therefore, Q2 = $64

The upper quartile of the given data set will be the 21st data point.

Therefore, Q3 = $75

Forth quartile of the given data set will be equal to the maximum value in the data set. Therefore, Q4 =-$84

Step 8/14

g.

53 $ is the lower quartile of the given data set. So, 25% of the numbers in the data set are at or below 53 $.

Therefore, 75% of the students spent $ 53 or more on gas.

Step 9/14

h.

Inter quartile range of the given data set will be,

Q3 -Q1

=$22

Step 10/14

i.

53 $ is the lower quartile and 75 $ is the upper quartile of the given data set. 50% of the numbers in the data set lie between lower quartile and upper quartile.

Therefore, 50% of the students spent from $ 53 to $ 75 on gas.

Step 11/14

j.

The boundary for the lower outliers will be,

53- 1.5 x 22

=20

Step 12/14

k.

The boundary for the upper outliers will be,

75 + 1.5 x 22

=108

Step 13/14

l.

Any number below 20 will be a lower outlier. So, $ 17 is a lower outlier.

Any number above 108 will be an upper outlier. So, there is no upper outlier.

Therefore, there is 1 outlier.

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A. If the bank had compounded the interest quarterly for the three years, the interest rate would be divided by 4 (since there are 4 quarters in a year) and the number of compounding periods would be multiplied by 4. This is because the interest would be calculated and added to the account balance every quarter, rather than just once a year.

B. To represent the account balance if interest is compounded quarterly, we need to use the formula for compound interest with quarterly compounding:

A = P(1 + r/n)^(nt)

where A is the account balance, P is the principal (initial deposit), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4 for quarterly compounding), and t is the number of years (3).

Substituting the given values into the formula, we get:

A = 1500(1 + 0.085/4)^(4×3)

A = 1500(1.02125)^12

A ≈ $1,969.36

Therefore, the new expression for the account balance, in dollars, if interest is compounded quarterly is:

$1,969.36 = 1500(1 + 0.085/4)^(4×3)

The equation is given as n = c + 2

The plant grows c inches in the first week.

The plant grows n inches in the second week.

mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).

thе growth in thе seсond wееk (n) is said to be  2 inсhes more than thе growth in thе first wееk (c) from the given question.

The equation would be

n = c + 2

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Thus, option B, "The population mean is between 8 and 10," is the claim that is most supported by the interval.

Based on the given confidence interval of 6 to 14, we can say with 95% confidence that the true population mean falls between those values. Therefore, option B, "The population mean is between 8 and 10," is the claim that is most supported by the interval.

Option A, "The population mean is less than 15," and option E, "The population mean is more than 7," are also supported by the interval but are less specific than option B.

Option C, "The population mean is exactly 9," is not necessarily supported by the interval, as the true mean could be any value within the interval.

Option D, "The population mean is more than 17," is not supported by the interval, as the upper limit of the interval is only 14.

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A graph of the piecewise function is shown on the coordinate plane in the image attached below.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is decreasing over the interval x ≤ 1 and increasing over the interval x > 1.

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Answer:

Kyle needs 112 marks on his sixth test for the mean test grade to be 90.

Step-by-step explanation:

Let the marks Kyle needs for the sixth test be x.

The mean of all tests is given as 90. The formula for mean would be: (sum of marks obtained in each test)/(total number of tests)

which implies,

(90+83+75+84+96+x)/6 = 90,

(428+x)/6 = 90,

428+x = 540,

x = 112

Therefore, Kyle needs 112 marks on his sixth test for the mean test grade to be 90.

The sum of all values divided by the total number of values determines a dataset's mean (also known as the arithmetic mean, which differs from the geometric mean). It is the most widely applied central tendency measure and is frequently called the "average."

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Answer:

x=80

Step-by-step explanation:

x+12 and x+48 must equal 180 so 60 is the answer

60+12=72

60+48=108

72+108=180

Answer: 60

Step-by-step explanation:

When you have 2 parrallel lines the angles will either be = or =180 in this case =180

so

A+B=180

x + 12 + x + 48 = 180

2x + 60 =180

2x = 120

x=60

The probability that sum of the two dice on a roll is 5 given that the blue die for that roll landed on 6 is 0.25 or 25%.

If we know that the blue die landed on 6, then we only need to consider the possible outcomes of the roll of the red die that would result in a sum of 5.

If red die shows 1, 2, 3 or 4, then the sum of the dice will be 6. There are a total of 6 possible outcomes for the roll of the red die (since it is a standard 6-sided die), but we can eliminate the outcomes 5 and 6 since they would result in a sum greater than 5.

So, out of the 4 possible outcomes for the roll of the red die that would result in a sum of 5, only one of them will occur if the blue die landed on 6. Therefore, the probability of getting a sum of 5 given that the blue die landed on 6 is:

1/4 = 0.25 or 25%

Hence the probability of the sum being 5 is 0.25 or 25%.

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