How does 8 × 2 1 3 compare to 8? A) Less than 8 because you are multiplying by number less than 1. B) Greater than 8 because you are multiplying by a number less than 1. C) Less than 8 because you are multiplying by a number greater than 1. D) Greater than 8 because you are multiplying by a number greater than 1.

The correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance

Based on the given information, we can conclude that there is a positive correlation between the number of hours studied per week and academic performance of 25 UK University students. The correlation coefficient of 0.71 suggests a moderate to strong positive relationship between the two variables. This means that as the number of hours studied per week increases, the academic performance of the students also tends to increase. However, it is important to note that the "critical r" value of 0.87 with a significance level of p≤0.05 indicates that there is a chance of 5% that the observed correlation between the variables could be due to random chance. This means that while the correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance, but it is not the only factor that contributes to success. Other variables such as natural ability, motivation, and study habits may also play a role in academic achievement.

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The correct value of the various questions is as follows:

2.) The table that shows the monthly rate for gym membership = Table C.

3.) The amount of money that Todd's mother bought the can vegetables = $10.50. That is option B.

4.) The amount of time it will take the reading group to read 80 pages = 60 mins . That is option D.

5.) The amount of money that Elliott spends of the protein bars at the gym = $13.75.

For question 2.)

The table that shows the monthly rate for gym membership = Table C. This so because;

1 month = $65

2 months = 65×2 = $130

8 months = 65×8 = $520

10 months = 65×10 =$650

For question 3.)

From the number line;

The cost of 4 cans = $3

14 cans = X

Make X the subject of formula ;

X = 14× 3/4

X = 42/4

X = $10.50

For question 4.)

For 8 pages = 6 minutes

80 pages = X

make X the subject of formula;

X = 80×6/8

X= 60 minutes.

For question 5.)

For 5 protein bars = $6.25

11 protein bars = X

make X the subject of formula;

X = 11× 6.25/5

X = 68.75/5

X= $13.75

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Answer: 5 dimes 4 nickels 12 quarters

Step-by-step explanation:

i dont think u need one bro

Beth has 7.5 Dimes, 6.5 Nickel, and 14.5 Quarters.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Total value =$3.70

Let

Nickel = x -1

Dimes =  x

Quarters = x + 7

Every

Nickel = 5 cents

Dimes = 10 cents

Quarters = 25 cents

Total cents = $3.70× 100 = $370

⇒ 5n + 10d + 25q = 370

⇒ 5(x-1) + 10(x) + 25(x+7) = 370

⇒ 5x-5 + 10x + 25x+175  = 370

⇒ 40x + 70= 370

⇒ 40x = 370 - 70

⇒ 40x = 300

Divide both sides by 40

⇒ x= 300/40

⇒ x = 7.5

⇒ Dimes =  7.5

⇒ Nickel = 7.5 -1 = 6.5

⇒ Quarters = 7.5 + 7 = 14.5

Hence, Beth has 7.5 Dimes, 6.5 Nickel, and 14.5 Quarters.

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Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:

1) inverse: x - 12

2) inverse: 3x + 6

3) inverse: x/2 - 6

4) inverse: x/3 + 4/3

5) inverse: 3x - 3/2

6) inverse: -3x/2 + 15/2

7) inverse: x/5 - 3

8) inverse: 2x/5 + 1/5

Statistically significant evidence exists against the manufacturer's claim of 1% defective laptops. The result is practically significant, indicating a higher defect rate with potential consequences for reputation and customer satisfaction.


According to the information given, the manufacturer claims that only 1% of their laptops are defective. However, in a sample of 600 computers, it was found that 3% were defective. To determine if there is statistically significant evidence against the manufacturer's claim, we need to conduct a hypothesis test.
1. Hypotheses:
  - Null Hypothesis (H0): The proportion of defective laptops is 1%.
  - Alternative Hypothesis (H1): The proportion of defective laptops is not 1%.
2. Test Statistic:
  We can use the Z-test for proportions to compare the sample proportion (3%) to the claimed proportion (1%). The formula for the test statistic is:
  Z = (p - p0) / √(p0 * (1 - p0) / n)
  where p is the sample proportion, p0 is the claimed proportion, and n is the sample size.

3. Calculation:
  In this case, p = 3% = 0.03, p0 = 1% = 0.01, and n = 600. Plugging these values into the formula, we can calculate the test statistic Z.

  Z = (0.03 - 0.01) / √(0.01 * (1 - 0.01) / 600)
  Z = 0.02 / √(0.01 * 0.99 / 600)
  Z ≈ 2.72
4. Conclusion:
  To determine if there is statistically significant evidence against the manufacturer's claim, we compare the test statistic Z to the critical value at a chosen significance level (e.g., α = 0.05). If the test statistic falls within the critical region, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the critical value for a two-tailed test at α = 0.05 is approximately ±1.96. Since the test statistic Z (2.72) falls outside the critical region (greater than 1.96), we reject the null hypothesis. Therefore, there is statistically significant evidence against the manufacturer's claim.

5. Practical significance:
  While the result is statistically significant, it is important to consider practical significance as well. The sample proportion of 3% being higher than the claimed proportion of 1% suggests a higher rate of defective laptops. This finding has practical significance as it indicates a potential issue with the quality control of the manufacturer's laptops. The higher rate of defects could impact customer satisfaction, warranty claims, and overall reputation of the brand.

In summary, based on the statistical analysis, there is statistically significant evidence against the manufacturer's claim of only 1% defective laptops. The result also has practical significance, suggesting a higher rate of defects that may have implications for the manufacturer's reputation and customer satisfaction.

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The confidence level for this poll is 95%. The remaining 5% represents the potential margin of error or uncertainty in the estimation.

The confidence level refers to the level of certainty or reliability we have in the results obtained from a survey or poll. It represents the probability that the true population parameter falls within a certain range based on the sample data collected. In this case, the confidence level is 95%, which is a commonly used value in statistical analysis.

To calculate the confidence level, we need to consider the margin of error and the sample size. The margin of error is given as 4.3%, which represents the maximum expected difference between the survey results and the true population parameter. The sample size is stated as 1001 American adults.

For a large sample size like this, we can use the formula:

Confidence level = 1 - (Margin of error / √(sample size))

Plugging in the values, we have:

Confidence level = 1 - (0.043 / √1001) ≈ 0.95

Converting this to a percentage, we get a confidence level of approximately 95%. This means that we can be 95% confident that the true proportion of Americans who believe marijuana and alcohol should have the same level of governmental regulation lies within the range obtained from the survey results. The remaining 5% represents the potential margin of error or uncertainty in the estimation.

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Answer:

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

Step-by-step explanation:

Answer:

18 ft = 6 yd

Step-by-step explanation:

Recall that 1 yd = 3 ft.

Thus, 18 ft is 6 times greater than 3 ft, and 18 ft becomes

18 ft       x

------- * ------

 3 ft     1 yd

Then 3x = 18, and x = 6.  

18 ft = 6 yd

c=14+xh is the  equation that represents the relationship between h and c.

An expression is combination of variables, numbers and operators.

Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.

Let h represent the duration of a rental in hours and c represent the total cost of the rental.

We have to find the  relationship between h and c.

c=14+xh

Here x represents the dollar.

Hence, c=14+xh is the  equation that represents the relationship between h and c.

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The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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Answer:

0.714

Step-by-step explanation:

5/7

(5X100) / 7 = 500/7.

50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.

10/7 = 1 remainder 3.

we have 71 remainder 3.

3/7: 300/7 = 42.83

we now have answer of 0.714282

= 0.714 to nearest thousandth

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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Answer:

O c.92

Step-by-step explanation:

if its incorrect im sorry <3

Answer:

52+28= 80 feet

Step-by-step explanation:

52 =26x2

so

14x2 = 28

Answer:

x =0   x=7

Step-by-step explanation:

x^2 - 7x=0

Factor out an x

x(x-7) =0

Using the zero product property

x =0   x-7 =0

x =0   x=7

Answer: 1/6

Step-by-step explanation:

An easy way for me to find a common denominator is to multiply both denominators: 3 times 2 and then subtract 2-1.

1/6  

i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).

j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).

i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).

j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).

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Answer:

2 hours and 30 minutes.

Step-by-step explanation:

First you must add $50 and $75. Then add two $75, to get $200. Then, Multiply $1.25 by 30.

Hope this helps :)

(If it did please make this brainliest.)

Answer:

Step-by-step explanation:

If f and g are inverse functions, then f (x) = y if and only if g (y) = x In trigonometry, the inverse sine function is used to find the measure of angle for which sine function generated the value. For example, sin-1(1) = sin-1(sin 90) = 90 degrees.

Answer:

Step-by-step explanation:

I'll just write log for log base 10.  The important rules about logarithms we need to know are:

\( a \log b = \log( b^a) \)

\( \log a + \log b = \log( ab) \)

and at the end we'll need something like

\(\log a = \log b \implies a=b\)

Suitably armed we can begin,

\( \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) \)

First rule,

\( \log 3^{ 1 + 1/2x}  + \log 2 = \log (27 - 3^{1/x}) \)

Second rule,

\( \log 2(3^{ 1 + 1/2x})  = \log (27 - 3^{1/x}) \)

Third rule,

\( 2(3^{ 1 + 1/2x})  = 27 - 3^{1/x} \)

We can rewrite this to be a quadratic equation in \(y=3^{1/2x}\).

\(  6 (3^{1/2x})  = 27 -  (3^{1/2x})^2 \)

\(y^2 +6y - 27 =0\)

\((y - 3)(y+9)=0\)

\(y=3 \textrm{ or } y=-9\)

First solution:

\(3^{1/2x} = 3 = 3^{1}\)

\(1/2x = 1\)

\(1=2x\)

\(x = 1/2\)

Second solution,

\(3^{1/2x} = -9\)

No real powers of 3 will be negative, no solution here.

Answer: x=1/2

Check:  

1 + 1/2x = 2 so the left side is log 2(3²) = log 18

Right side, log(27-3^2) = log 18  √

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the industry's output is Y = 3, and the profit of each firm  = -2.

a) Supply curve of an individual firm

The price received by the individual firm will be P. Its demand curve is given by

D(p) = 20 - p.

Each firm chooses output to maximize its profit. Profit maximization occurs when the price is equal to the marginal cost. Mathematically,

P = MC(y)

4y = P

y = P/4

Thus the supply curve of the firm is y = P/4

b) The smallest price at which the product can be sold. The product can be sold at the minimum of the supply curve, which is y = 0, given P ≥ 0. Therefore the smallest price is P = 0.

c) Equilibrium price and output

Equilibrium occurs when each firm is producing at its profit-maximizing output given the output of other firms. Let the number of firms in the industry be n. The output of the industry is Y = ny. The industry supply curve is given by

S(P) = nP/4

The equilibrium price intersects the industry supply curve with the demand curve. Thus the equilibrium price satisfies

S(P) = Y

nP/4 = 20 - P

=> P = 80/(4 + n).

The equilibrium number of firms is the number that makes the industry supply curve equal to the demand curve. Thus

20 - P = nP/4

=> P = 80/(4 + n)

=> n = (80 - 20P)/P

= 20/P - 4.

Thus the equilibrium number of firms is a function of P and can range between 1 and infinity, but it must be an integer. The equilibrium output of each firm is given by

y = P/4 = 20/(4n + n²)

The equilibrium output of the industry is given by

Y = n

y = 5/P = (n² + 4n)/80.

d) Equilibrium number of firms with new demand curve D(p) = 21 - p.

The intersection of this curve with the marginal cost curve is at p = 21/5. This is greater than the minimum possible price of 0. Thus there is a positive profit to be earned in this industry, and new firms can enter the market.

e) Equilibrium price and output with new demand curve with the new demand curve D(p) = 21 - p, the industry supply curve and the equilibrium price are as given in part (d). The equilibrium output of each firm is given by y = P/4 = 21/20, and the equilibrium output of the industry is given by Y = 21/4.

f) Equilibrium number of firms, price, output, and profit with demand curve D(p) = 24 - p. This demand curve intersects the marginal cost curve at p = 6. The minimum possible price is P = 0. Thus there is a range of prices from 0 to 6 where firms can profit positively.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the output of the industry is Y = 3, and the profit of each firm is (6)(3/2) - (2)(2(3/2)² + 8) = -2.

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

A

Step-by-step explanation:

A(√-2) is a complex number. Complex numbers are not real numbers. Therefore A is not a real number.

To guess a particular solution up to the term involving the highest power of u and its derivatives, we assume that the particular solution has the form:

u_p = a(x) + b(x)y

where a(x) and b(x) are functions to be determined.

Substituting this into the given equation:

u^2 + 2xu(dy/dx) = 2x^2

Expanding the terms and collecting like terms:

(a + by)^2 + 2x(a + by)(dy/dx) = 2x^2

Expanding further:

a^2 + 2aby + b^2y^2 + 2ax(dy/dx) + 2bxy(dy/dx) = 2x^2

Comparing coefficients of like terms:

a^2 = 0        (coefficient of 1)

2ab = 0        (coefficient of y)

b^2 = 0        (coefficient of y^2)

2ax + 2bxy = 2x^2        (coefficient of x)

From the equations above, we can see that a = 0, b = 0, and 2ax = 2x^2.

Solving the last equation for a particular solution:

2ax = 2x^2

a = x

Therefore, a particular solution up to u^2 + 2xuy is:

u_p = x

To find the general solution, we need to add the homogeneous solution. The given equation is a first-order linear PDE, so the homogeneous equation is:

2xu(dy/dx) = 0

This equation has the solution u_h = C(x), where C(x) is an arbitrary function of x.

Therefore, the general solution to the given PDE is:

u = u_p + u_h = x + C(x)

where C(x) is an arbitrary function of x.

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Answer:

Put your dot on 7/4 and then then -1 means you will go left 1 time and down 1 time 1 left 1 down it should look like a staircase

Step-by-step explanation:

The probability of a value falling between these two z-scores is 68%. and The probability is 2.3%.

Probability is the measure of likelihood that something will happen. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. Probability is used to describe random events, such as the outcome of a coin toss or the roll of a die. It is also used to describe events that are not random, such as the likelihood of a certain person being elected to a political office.

a. About 68% of houseflies have wing lengths between 3.8 millimeters and 5.0 millimeters.
This is calculated using the z-score formula, z=(x-μ)/σ, where x is the given value, μ is the mean, and σ is the standard deviation.
In this case, z=(3.8-4.6)/0.4 = -1.5 and z=(5.0-4.6)/0.4 = 0.5.
Using a z-score table, we can find that the probability of a value falling between these two z-scores is 68%.

b. About 2.3% of houseflies have wing lengths longer than 5.8 millimeters. This is calculated by taking the z-score for 5.8 millimeters (z=(5.8-4.6)/0.4 = 1.5) and finding the probability from the z-score table. The probability is 2.3%.

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