I need help with this please

Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.

Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.

This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.

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The n-th trianglar number is given by

\(T_n = \dfrac{n(n+1)}2\)

Then

\(T_4 + T_3 = \dfrac{4\times5}2 + \dfrac{3\times4}2 = \boxed{16}\)

Alternatively, the triangular numbers are defined recursively by

\(\begin{cases}T_1 = 1 \\ T_n = T_{n-1} + n & \text{for } n>1\end{cases}\)

This means

\(T_1=1\)

\(T_2 = T_1 + 2 = 3\)

\(T_3 = T_2 + 3 = 6\)

\(T_4 = T_3 + 4 = 10\)

so that

\(T_3+T_4=\boxed{16}\)

The estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%.

The conviction rate for speeding in the county is 85%, it means that out of every 100 speeding summonses issued, 85 are likely to result in convictions. Therefore, we can assume that the probability of a conviction in any given case is 0.85 or 85%.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we can use the binomial distribution formula. Let X be the number of convictions out of the 100 summonses. Then,

P(X ≥ 90) = 1 - P(X < 90)
           = 1 - Σ P(X = i) for i = 0 to 89

where Σ denotes the sum from i = 0 to 89.

Using the binomial distribution formula, we can calculate the probability of getting exactly i convictions out of 100 summonses as:

P(X = i) = (100 choose i) * 0.85^i * 0.15^(100-i)

where (100 choose i) denotes the binomial coefficient, which represents the number of ways to choose i items out of 100.

Plugging this formula into the above equation and using a calculator or statistical software, we get:

P(X ≥ 90) = 1 - Σ P(X = i) for i = 0 to 89
           = 1 - 0.0003 (approx.)
           = 0.9997 (approx.)

Therefore, the estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%. This suggests that it is highly likely that at least 90 out of 100 speeding summonses will result in convictions, given the high conviction rate of 85% in the county.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we'll use the binomial probability formula:

P(X ≥ 90) = Σ [C(n, k) * p^k * (1-p)^(n-k)]

Here, n = 100 (number of summonses), p = 0.85 (conviction rate for speeding), and k represents the number of successful convictions (90 to 100).

Step 1: Calculate the individual probabilities for k = 90 to 100:
For each value of k from 90 to 100, compute the binomial probability using the formula. C(n, k) represents the number of combinations of choosing k convictions from n summonses.

Step 2: Sum the individual probabilities:
Add up the probabilities calculated in Step 1 to find the total probability of having at least 90 convictions out of 100 speeding summonses.

By following these steps, you can estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

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Answer:

$4.70

Step-by-step explanation:

3*5.10= 15.30

20-15.30= 4.7

Answer:

she should get $4.70

Step-by-step explanation:

you need to take 5.10 and multiply by 3 to get $15.3 then do 20 minus 15.30

The answer is -300 because he owes -225 and then when he spends they subtract the amount he spent so the equation would be -225-75= the answer of -300

Answer:

Step-by-step explanation:

The mathematical translation of the statement:

\(\sqrt{121} = \sqrt{11 *11}\)

        \(= \sqrt{11^{2}}\)

        \(= (11^{2}) ^{\frac{1}{2} }\)

The indices will cancel each other out completely:

        \(= 11\)

OR:

\(\sqrt{121} = \sqrt{(-11)*(-11)}\)

        \(= \sqrt{(-11)^{2} }\)

        \(= [(-11)^{2}] ^{\frac{1}{2} }\)

        = -11

Answer:

5 is small 6 is bigger

Step-by-step explanation:

because 6 is bigger and 5 is small than divide

Answer:

1072

Step-by-step explanation:

Answer:

$50678.73

Step-by-step explanation:

Answer:

103,078.73.

Step-by-step explanation:

Amount after n years = P(1 + r/100)^n       where P is amount invested, r is the percentage rate and n = number of years.

So, here we have:

Total after 10 years = 52400(1 + 7/100)^10

= 52400 * 1.967151357

= 103,078.73.

Answer:

u should times 24 by 24 which will make 576

Step-by-step explanation:

the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Answer:

34

Step-by-step explanation:

you first write the equation:

(8-3) / (8+x-7) = 1/7, where x is the number of non blue socks

so, 5/(1+x) = 1/7

1+x = 35, so x=34

The more economical purchase is the 24-ounce box of cornflakes for $3.89.

The more economical purchase can be determined by calculating the unit rate for each box of cornflakes.

The unit rate can be calculated by the division of the total ounce of the box by the price of the box

Hence the unit rate for the 18-ounce box is calculated as,

unit rate of 18-ounce box = 18 / 3.49

unit rate of 18-ounce box = 5.16 ounce/$

The unit rate for the 24-ounce box is calculated as,

unit rate of 24-ounce box = 24 / 3.89

unit rate of 24-ounce box = 6.17 ounce/$

As the rate of 6.17 ounce/$ is more economical than 5.16 ounce/$, the more economical purchase is the 24-ounce box of corn flakes.

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Answer:

Step-by-step explanation:

hello,

As A and B are two independent events we can say that P(A∩B)=P(A)P(B)

P(A)=P(A∩B)/P(B)=16/13

thanks

The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.

To construct the desired polynomial, we know that since it has downward end behavior on both sides, the leading coefficient must be negative. Moreover, since there are three x-intercepts, the polynomial must have three linear factors corresponding to those intercepts.

Let's denote the polynomial as f(x). Since it has x-intercepts at -5, 1, and 4, the factors of the polynomial can be written as (x + 5), (x - 1), and (x - 4). To ensure downward end behavior, we need to multiply these factors by two additional linear factors. We can choose (x - a) and (x - b), where a and b are large positive values.

Therefore, the equation of the 4th-degree polynomial satisfying the given conditions is:

f(x) = -(x + 5)(x - 1)(x - 4)(x - a)(x - b)

The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.

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Answer:

1/2 teaspoon salt

Step-by-step explanation:

We can make this into a ratio of salt:baking soda

1/8:1/4

now, how many 1/4 will we need to make 1?

If we multiply 1/4 by 4, we get one. So, we should do the same to 1/8!

1/8*2=4/8, or 1/2 teaspoon

Answer:

A) total area = 364ft²

B) total cost = $2,184

Step-by-step explanation:

total area of the brick paver border that surrounds the pool

= w * h = 14 * 26 = 364ft²

if brick pavers cost $6 per square foot

total cost of the brick pavers needed for this project

= 364 * 6 = $2,184

Answer:

  y +7 = 3(x +4)

Step-by-step explanation:

You want the point-slope equation of the line with slope 3 through point (-4, -7).

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For m=3 and (h, k) = (-4, -7), this is ...

  y -(-7) = 3(x -(-4)) . . . . . substitute for m, h, k

  y +7 = 3(x +4)

1) It will take 40 minutes to fill the same tank with 2 pumps

2) the product of the means equals the product of the extremes".

3) Tes is 56 years old, given that the ratio of their ages is 3:7

4) 10 the value of N in the expression

5) 150 is the bigger number if the sum of the numbers is 240, and the ratio is 3:5

1) time × speed = time × speed

= 16 × 5 = x × 2

= \(\frac{16*5}{2}\) = x

x = 80\2

x = 40 minutes

2) product

ab=cd. the product of the means equals the product of the extremes. That is, ad=bc. We can get an equivalent result using a technique called cross multiplication.

3) let the age of ed be x, then age of tes is 80 - x

\(\frac{x}{80-x}\) = \(\frac{3}{7}\)

7x = 3(80-x)

7x =  240 - 3x

7x + 3x = 240

10x = 240

x = 24

Ed's age is 24 therefore Tes age is 80 - x

80 - 24 = 56

therefore tes age is 56

4) 2\7 = N\35

2 × 35\ 7 = N

70\7 = N

N = 10

5) Let the multiple of the ratio be x

3x + 5x = 240

8x = 240

x = 30

we need to find the bigger number therefore,

5x = 5 × 30 = 150

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The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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Answer:

5.213

Step-by-step explanation:

bruh just search up right triangle calculator

Part A:

I got the number of kids in the survey which is 130 and I found 70 which is the amount of kids who like playing on a pc/console. I took 130 and 70 and converted it into a fraction 70/130, I simplified it to 7/13 and used a calculator to get my percentage which I rounded and got 53%

Part B:

I drew a table and just focused on column two. I looked at how many people don't like phone or pc and I found that 10 is how many people like phone and not pc, 30 is people who dont like phone or pc, together its 40, so you need to find what the percentage 30 is of 40, or 3/4, I used a calculator and converted it into a percentage and I got 75%

Answer:

3 the answer is 3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The solution is,  the measure of ∠ZYC is 108 degrees.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

Given:

m∠XYZ = 72 degrees

m∠XYZ and m∠ZYC form a linear pair.

Let's find the measure of ∠ZYC.

To find the measure of angle ZYC, apply the Linear Pair of Angles theorem which states that the sum of angles that form a linear pair is 180 degrees.

Hence, we have:

m∠XYZ + m∠ZYC = 180

72 + m∠ZYC = 180

• Subtract 72 from both sides:

72 - 72 + m∠ZYC = 180 - 72

m∠ZYC = 180 - 72

m∠ZYC = 108 degrees.

Therefore, the measure of ∠ZYC is 108 degrees.

ANSWER:

C. 108°

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Complete question:

If ZXyz and ZZYC form a linear pair and the measure of ZXYZ is 72°, whatis the measure of ZZYC?O A. 28°B. 18°C. 108°D. 72°

The coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .

Let

OA vector = ( - 5 , - 7 )

OA' = 2 ( -5 , - 7 )

A' = ( - 10 , - 14 )

OB vector = ( 6 , - 3 )

OB' vector = 2 ( 6 , - 3 )

B' = ( 12 , - 6 )

OC vector = ( 2 , 7 )

OC' vector = 2 ( 2 , 7 )

c' = ( 4 , 14 )

Hence , the coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .

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Answer:

- 2/3 is the answer

Step-by-step explanation:

You are told that you will have to wait for 5 hours in a line with a group of other people. The number of minutes you have to wait is 300 minutes.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

It is a quantity that is a part of several measures that are used to compare the length of events or the gaps between them, to compare how long they last, to order events, and to measure how quickly things change in the actual world or in our conscious experience. You are told that you will have to wait for 5 hours in a line with a group of other people. The number of hours you have to wait is 300 minutes.

1 hour = 60 minutes

          =5×60

         = 300  minutes

Therefore, the number of hours you have to wait is 300 minutes.

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Answer:

The coordinate of the circumcenter of the given triangle is (4, -1)

Step-by-step explanation:

The circumcenter is found by the intersection of the perpendicular bisectors of a triangle as follows;

The vertices of triangle ΔABC are A(1, 1), B(1, -3), and C(7, -3)

The coordinates of the midpoint of segment AB is 1/2(1 + 1, 1 + (-3)) = (1, -1)

The slope of segment AB = ∞, therefore, the slope of the perpendicular to segment AB = -1/∞ = 0

The line representing the perpendicular to segment AB is y = -1

The coordinates of the midpoint of segment BC is 1/2(1 + 7, (-3) + (-3)) = (4, -3)

The slope of segment BC = 0, therefore, the slope of the perpendicular to segment BC = ∞, which is a vertical line parallel to the y-axis with equation, x = 4

Therefore, the coordinate of the circumcenter is the intersection of the lines y = -1, and x = 4, which is the point (4, -1).