Commuting. there are two routes he could take to work. Aneighbor who has lived there a long time tells him Route Awill average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to go, driving each route 20 days. He finds that Route Atakes an average of 40 minutes, with stan- dard deviation 3 minutes, and Route B takes an average of 43 minutes, with standard deviation 2 minutes. His- tograms of travel times for the routes are roughly sym- metric and show no outliers. a.Find a 95% confidence interval for the difference in average commuting time for the two routes. b.Should the man believe the old-timer s claim that he can save an average of 5 minutes a day by always driving Route A

Answer:

4/5

Step-by-step explanation:

We can find the slope when given two points by using

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

  = (8-0)/(10-0)

  =8/10

  = 4/5

Answer:

4/5

Step-by-step explanation:

Answer:

the answer is 44

you don't have the answer choice

Answer:

use [tex]a = 1/4\pi d^2\\[/tex]

all you have to do is plug 4 into d and then square it, and multiply everything together.

Step-by-step explanation:

Answer:

78 ml of 7% vinegar and 312 ml of 12% vinegar.

Step-by-step explanation:

Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.    

We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:

[tex]x+y=390...(1)[/tex]

[tex]y=390-x...(1)[/tex]

We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be [tex]0.07x[/tex].

The second brand contains 12 vinegar, so amount of vinegar in y ml would be [tex]0.12y[/tex].

We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:

[tex]0.07x+0.12y=390(0.11)...(2)[/tex]

Upon substituting equation (1) in equation (2), we will get:

[tex]0.07x+0.12(390-x)=390(0.11)[/tex]

[tex]0.07x+46.8-0.12x=42.9[/tex]

[tex]-0.05x+46.8=42.9[/tex]

[tex]-0.05x+46.8-46.8=42.9-46.8[/tex]

[tex]-0.05x=-3.9[/tex]

[tex]\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}[/tex]

[tex]x=78[/tex]

Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.

Upon substituting [tex]x=78[/tex] in equation (1), we will get:

[tex]y=390-78[/tex]

[tex]y=312[/tex]

Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.

Answer:

A is a countable set

Step-by-step explanation:

Assume B is a countable set, Go through the attached file for a detailed step by step explanation of the proof that A is a countable set.

Answer:

$70.77

Step-by-step explanation:

A=8.09s+3.79c

A=8.09(5)+3.79(8)

A=40.45+30.32

A=70.77

Answer:

$70.77

Step-by-step explanation:

5s+8c=?

5(8.09) + 8(3.79) = ?

40.45 + 30.32 = ?

$70.77

Answer:

The actual Answer is 10x5=50

Answer: 50

Step-by-step explanation: it’s like when you get 10 and add it up 5 times you get 50

Answer:

C. 31

Step-by-step explanation:

(570.7 - n) ÷ 16

(570.7 - 74.7) ÷ 16

496 ÷ 16

31

Answer:

6(1-r)

Step-by-step explanation:

8-6r+2

=6-6r

=6(1-r)

Answer:

$220?

Step-by-step explanation:

Answer$220

Step-by-step explanation:

77/7=$11 so $11x20=220

Answer:

x ≥ -53

Step-by-step explanation:

There is a closed circle at -53 which means equal to

The line goes to the right which means greater than

x ≥ -53

Answer:

D) x>=-53

Step-by-step explanation:

A closed dot means -53 is included in the inequality as a solution, and since it's going right, it's greater than or equal to -53.

Answer:

The answer is there is a difference in the mean production rate by shift

Step-by-step explanation:

The level of significance is actually very low since the same production level is maintained for each of the 5 workers at the same time in the afternoon.

As for the other shifts, that is, the day shift and the night shift, the level of significance varies according to the production established by each worker.h

Answer:

[tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = \frac{5}{4}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \frac{10}{x^2} \\\left[ 4 ,\ 8 \right][/tex]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Final answer:

To solve 3km 6hm 7dam 5m ÷ 15, first convert the distance to meters (3675 m) and then divide by 15 to get 245 meters.

Explanation:

The question given by the student involves performing a division operation with a composite distance measurement in different units. First, we need to convert the entire distance into a single unit (meters) before we divide it by the given number (15).

To convert the given distance to meters, we use the metric system unit conversion:
1 kilometer (km) = 1000 meters (m), 1 hectometer (hm) = 100 meters (m), and 1 decameter (dam) = 10 meters (m). Therefore, 3 km is 3000 m, 6 hm is 600 m, 7 dam is 70 m, and adding the given 5 m to these conversions, we get a total distance of 3675 meters (3000 m + 600 m + 70 m + 5 m = 3675 m).

To find the final answer, divide 3675 meters by 15: which yields 245 meters. Thus, 3km 6hm 7dam 5m divided by 15 equals 245 meters.

Answer:

Slope (m)= -12.5/5= -2.5

-12.5/5 in fraction form

or

-2.5 in decimal form

Step-by-step explanation:

slope (m)= -12.5/5= -2.5

the points belong as a decreasing linear function

equation: y= -2.5x-5

Answer:

-5(3x^3-1)

Step-by-step explanation:

-15x^3+5

Factor out -5

-5(3x^3-1)

Answer:

a) [tex]L(t) = 3 + 2\cdot t[/tex], b) [tex]S (t) = 3\cdot t[/tex], c) Third day.

Step-by-step explanation:

a) The equation to represent Layla's fees is:

[tex]L(t) = 3 + 2\cdot t[/tex]

b) The equation to represent Sam's fees is:

[tex]S (t) = 3\cdot t[/tex]

c) Both earn the same amount for dog sitting at the third day.

Final answer:

To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, use the Central Limit Theorem to approximate the distribution of sample means. Calculate the standard error using the formula: standard error = population standard deviation / sqrt(sample size). Then, standardize the sample mean using the z-score formula. Finally, find the probability using a standard normal distribution table or a calculator.Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.

Explanation:

To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).

First, we need to calculate the standard error, which is the standard deviation of the sampling distribution of the sample mean. The standard error is given by the formula: standard error = population standard deviation / sqrt(sample size). In this case, the population standard deviation is 368 miles, and the sample size is 44. Therefore, the standard error = 368 / sqrt(44) = 55.354 miles.

Next, we use the z-score formula to standardize the sample mean. The z-score = (sample mean - population mean) / standard error. Plugging in the given values, we get: z-score = (51 - 2643) / 55.354 = -0.3668.

Finally, we need to find the probability that the standardized sample mean (z-score) is less than -0.3668. We can use a standard normal distribution table or a calculator to find the corresponding probability. From the standard normal distribution table, we find that the probability corresponding to a z-score of -0.3668 is approximately 0.3595. Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.

Answer:

the 90% of confidence intervals for the average salary of a CFA charter holder

 (1,63,775 , 1,80,000)

Step-by-step explanation:

Explanation:-

random sample of n = 49 recent charter holders

mean of sample (x⁻) =  $172,000

standard deviation of sample( S) = $35,000

Level of significance α= 1.645

90% confidence interval

[tex](x^{-} - Z_{\alpha } \frac{s}{\sqrt{n} } , x^{-} + Z_{\alpha } \frac{s}{\sqrt{n} })[/tex]

[tex](172000 - 1.645 \frac{35000}{\sqrt{49} } , 172000 +1.645 \frac{35000}{\sqrt{49} })[/tex]

on calculation , we get

(1,63,775 , 1,80,000)

The mean value lies between the 90% of confidence intervals

(1,63,775 , 1,80,000)

Answer:

The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505

Step-by-step explanation:

Mean defect length = u = 32

Standard deviation = [tex]\sigma[/tex] = 7.3

The distribution is normal and we have the value of population standard deviation so we will use the concept of z-score and probability from z-table to find the said probability.

We have to find the probability that the defect length is at most 20 mm. At most 20 mm means equal to or lesser than 20 mm. Since the normal distribution is a continuous distribution, the probability of at most is approximately equal to probability of lesser than.

If X represents the distribution of defect lengths, then we can write:

P(X ≤ 20) ≅  P(X < 20)

We can find the probability of defect length being lesser than 20 mm by converting it to z-score and find the corresponding probability from the z-table.

The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting the values, we get:

[tex]z=\frac{20-32}{7.3}=-1.64[/tex]

Therefore, P(X < 20) is equivalent to P(z < -1.64)

From z-table we can find the probability of z being lesser than - 1.64, which comes out to be:

P(z < -1.64) = 0.0505

Therefore, we can conclude that:

The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505

Answer:

[tex](D)E[ X ] =np.[/tex]

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success​ p,

[tex]f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n[/tex]

[tex]E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}[/tex]

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

[tex]E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}[/tex]

Now,

[tex]x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)[/tex]

Substituting,

[tex]E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}[/tex]

Factoring out the n and one p from the above expression:

[tex]E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}[/tex]

Representing k=x-1 in the above gives us:

[tex]E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}[/tex]

This can then be written by the Binomial Formula as:

[tex]E[ X ] = (np) (p +(1 - p))^{n -1 }= np.[/tex]

The correct formula for the expected number of successes in a binomial experiment with n trials and probability of success p is μ = np (Option D), which means that the expected number of successes is calculated by multiplying the total number of trials by the probability of success.

The formula for the expected number of successes in a binomial experiment with n trials and probability of success p is given by μ = np. In this formula, 'n' represents the number of trials, and 'p' is the probability of success on each trial. Therefore, the correct option, in this case, is D. Upper E (Upper X ) equals np.

This essentially means that the expected number of successes is obtained by multiplying the total number of trials by the probability of success. For instance, if you were to flip a coin (where the probability of getting heads is 0.5) 10 times, the expected number of times you'd get heads would be 0.5 * 10 = 5.

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Answer:

The answer is option A.

Step-by-step explanation:

Subjective probability is defined as a probability which is derived from a person's own experience or belief without relying on any data or scientific calculation.

In the question, the situation given in option A is an example of subjective probability because the analyst is giving a probability based on his or her own belief without using any data at all.

The other options clearly state the probability is being calculated by relying on observations and data.

I hope this answer helps.

A subjective probability example is the belief of a sports analyst in the probability of one college team beating another, without prior data. This contrasts with objective probabilities based on statistical analysis or historical evidence.

The example of a subjective probability among the options given is when a sports analyst believes there is a 0.8 probability that College A will beat College B in their upcoming basketball game, despite there being no previous encounters between the two teams to base this on. This type of probability, which includes personal belief or judgment rather than empirical evidence and statistical analysis, contrasts with objective probabilities that rely on historical data, such as the probability of a 20-year old driver having an accident or the probability of drawing a specific card from a standard deck.

Subjective probability is used in situations where there is a lack of historical data or when assessing future events, making it a personal estimation. This approach is different from calculating probabilities based on observed outcomes and statistical independence, where the probability of events is determined through analysis and empirical evidence.

Yes, the equation specifies a function with independent variable​ x.

Equation: 6x + 19y = 7

This can be put in y = mx + b form,

6x + 19y = 7

19y = -6x + 7

y = -[tex]\frac{6}{19}[/tex]x + [tex]\frac{7}{19}[/tex]

Since the equation can be put in the form of a linear function, the domain is all read numbers (-∞,∞) or -∞ < x < ∞ .

The equation 6x + 19y = 7 does not specify a function in terms of x because for each value of x, there exist multiple possible values of y. A specific example is shown when x = 1.

The equation "6x + 19y = 7" does not specify a function with the independent variable x. In a function, each input (x) corresponds to exactly one output (y). However, in this equation, each value of x corresponds to multiple values of y, thus it does not represent a function.

In order to find a value of x for which there are multiple corresponding values of y, we can set x to any arbitrary value. For example, if we set x = 1, we get "6(1) + 19y = 7", which simplifies to "19y = 1". This implies that there are infinite solutions for y when x = 1, confirming that the equation does not represent a function.

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Answer:

w = [tex]-\frac{7}{6}u[/tex]

Step-by-step explanation:

If u will be the independent variable, then w will have to be made the subject of the equation so that w will depend on the changes in u

4u + 8w = −3u + 2w

First collect all like terms

8w − 2w = −3u − 4u

6w = −7u

divide both sides by 6

∴ w = [tex]-\frac{7}{6}u[/tex]

In the equation w = [tex]-\frac{7}{6}u[/tex] , U is independent variable.

Missing part of the question

b)What is the value of R?

Answer:

a. X = 155.2

b. R = 4.4

Step-by-step explanation:

a. Calculating the value of x.

The value of x is the mean of the mean observation; i.e. the mean column

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 158.9 + 151.2 + 155.6 + 155.5 + 154.6

Summation of Observation = 775.8

Number of Observations = 5

X = Mean = 775.8/5

X = 155.16

X = 155.2 ----- Approximated to 1 decimal place

b. Calculating the value of R.

The value of R is the mean/average of the Range

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 4.0 + 4.6 + 4.3 + 5.0 + 4.3

Summation of Observation = 22.2

Number of Observations = 5

R = Mean = 22.2/5

R = 4.44

R = 4.4 ----- Approximated to 1 decimal place

The average diameter [tex](\( \overline{x} \))[/tex] of the pistons from the provided data is 155.16 mm, calculated by summing the daily means and dividing by the number of days.

In the context provided, [tex]\( \overline{x} \)[/tex] refers to the average of the piston diameters measured across different days at Wemming Chung's plant.

To find this value, we need to calculate the mean of the daily means [tex](\( \overline{x} \))[/tex] which are 158.9, 151.2, 155.6, 155.5, and 154.6 mm. This is done by summing these values and dividing by the number of days (5 in this case).

[tex]\[ \overline{x} = \frac{158.9 + 151.2 + 155.6 + 155.5 + 154.6}{5} \][/tex]

[tex]\[ \overline{x} = \frac{775.8}{5} \][/tex]

[tex]\[ \overline{x} = 155.16 \text{ mm} \][/tex]

Hence, the value of  [tex]\( \overline{x} \)[/tex] is 155.16 mm.

The one line of symmetry is vertical, so we could fold the hexagon in half in such a way that the vertices A and B would meet at the same point, and the same goes for the pairs C,F and D,E. Because of this symmetry, we know angle AFE is congruent to BCD, and angle FED is congruent ot CDE.

Let x be the measure of angle CDE.

In any convex polygon with n sides, the interior angles sum to (n - 2)*180º in measure. ABCDEF is a hexagon, so n = 6.

We have 2 angles of measure 123º, 2 of measure x, and 2 of measure 2x. So

2(123º + x + 2x ) = (6 - 2)*180º

246º + 2x + 4x = 720º

6x = 474º

x = 79º

Angle AFE is congruent to angle BCD, which is twice the measure of CDE, so angle AFE has measure 2*79º = 158º.

Answer:

False

Step-by-step explanation:

Because with the lines on the outside automatically changes the number to a positive number so, therefor the numbers are equal hope this help.

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Michaela's statement that |3| is bigger than |-3| is true.

Michaela's assertion that |3| is greater than |-3| is accurate. The absolute value of a number represents its distance from zero on the number line. In this case, |3| signifies a 3-unit distance from zero, and |-3| also corresponds to a 3-unit distance from zero. Since both values are equidistant from zero, their magnitudes are equal. Consequently, |3| and |-3| both have a value of 3, emphasizing that the absolute value of a number signifies its distance from zero, regardless of its sign, and in this case, both distances are identical at 3 units.

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Answer:

The zeros for this function are x = -1 and x = 1.67

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = 3x^{2} - 2x - 5[/tex]

The zeros of the function are the values of x for which

[tex]f(x) = 0[/tex]

Then

[tex]3x^{2} - 2x - 5 = 0[/tex]

This means that [tex]a = 3, b = -2, c = -5[/tex]

Then

[tex]\bigtriangleup = (-2)^{2} - 4*3*(-5) = 64[/tex]

[tex]x_{1} = \frac{-(-2) + \sqrt{64}}{2*3} = 1.67[/tex]

[tex]x_{2} = \frac{-(-2) - \sqrt{64}}{2*3} = -1[/tex]

The zeros for this function are x = -1 and x = 1.67

Answer:

.55M + 75 = the total cost

.55(300) + 75 = $240

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

GIVEN: Nadia is making a rectangular moisac out of [tex]\frac{1}{2}[/tex] inch by [tex]\frac{1}{2}[/tex] inch tiles. The rectangle is [tex]12[/tex] inches long and [tex]3\frac{1}{2}[/tex] inches wide.

TO FIND: How many tiles will Nadia use to cover the rectangle completely.

SOLUTION:

Area of rectangular moisac[tex]=\text{length}\times\text{width}[/tex]

                                            [tex]=12\times3\frac{1}{2}=\frac{12\times7}{2}[/tex]

                                            [tex]=42 \text{ inch}^2[/tex]

Area of one   tile [tex]=\text{side}^2[/tex]

                           [tex]=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\text{ inch}^2[/tex]

According to question

Total tiles required [tex]=\frac{\text{Area of rectangular moisac}}{\text{Area of one tile}}[/tex]

                                [tex]=\frac{42}{\frac{1}{4}}=42\times4[/tex]

                                [tex]=168[/tex] tiles

Hence, 168 tiles are required to completely cover the rectangular moisac.