(Sec. 8.4) In a sample of 165 students at an Australian university that introduced the use of plagiarism-detection software in a number of courses, 55 students indicated a belief that such software unfairly targets students. Does this suggest that a majority of students at the university do not believe that it unfairly targets them? Test the appropriate hypotheses at the 5% significance level.

Answer:

Step-by-step explanation:

For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.

The amount of alcohol in the mix is ...

  0.22x +0.10(4.8-x) = 0.12(4.8)

Eliminating parentheses, we have ...

  0.22x -0.10x +0.10(4.8) = 0.12(4.8)

Subtracting (0.10)(4.8) and combining x-terms gives ...

  0.12x = 0.02(4.8)

  x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient

The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.

The fish tank, when filled halfway with a height of water at 5 inches, contains 1920 cubic inches of water based on its dimensions of 24 inches by 16 inches by 5 inches.

To calculate the volume of water in the fish tank when it is filled halfway, we need to use the tank's dimensions and consider only half the height, as it is filled to that level. The tank measures 24 inches long, 16 inches deep (width), and 10 inches tall. Since it is filled halfway, the water level is at 5 inches high.

Volume of the tank is calculated by the formula for the volume of a rectangular prism: Volume = Length × Width × Height. So we calculate half the volume: Volume = 24 inches × 16 inches × 5 inches. The calculations would be: 24 × 16 × 5 = 1920 cubic inches.

Therefore, the fish tank has 1920 cubic inches of water when filled halfway.

Answer:

14.46% probability that the instructor can finish grading in 4 and a half hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n values from a distribution, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex]

In this problem, we have that:

[tex]\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843[/tex]

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{270 - 300}{28.2843}[/tex]

[tex]Z = -1.06[/tex]

[tex]Z = -1.06[/tex] has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

Answer:

83.56/p

Step-by-step explanation:

Let the weight of the players = p

Let the weight of the reserve players = r

Since there 9 players, there weight = 9p

And since there 3 reserve players, there weight = 3r

(9p + 3r) / 12 = 188

9p + 3r = 12 * 188

9p + 3r = 2256

Solve for r

r = 2256 / 27p

r = 83.56/p

Answer:

The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.

Step-by-step explanation:

For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

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

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

In the city where she lives, the probability that an independent restaurant will fail in the first year is 43 %.

This means that [tex]p = 0.43[/tex]

66 independent restaurants

This means that [tex]n = 66[/tex]

Mean:

[tex]E(X) = np = 66*0.43 = 28.38[/tex]

Standard deviation:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = 4.02[/tex]

The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.

Answer:

81/16

Step-by-step explanation:

The simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The complete question is:

Evaluate this exponential expression:

[tex]\dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]

We have an exponential expression:

[tex]= \dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]

[tex]\rm =\dfrac{27^{\dfrac{4}{3}}}{8^{\dfrac{4}{3}}}[/tex]

[tex]=\dfrac{81}{8^{\dfrac{4}{3}}}[/tex]

= 81/16

Thus, the simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.

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Answer: Option D.

Step-by-step explanation:

this is a quadratic equation of the form:

y = ax^2 + bx + c

First, things you must see.

The graph opens up, so we must have thata a is greater than zero, so we can discard the first option.

Second, we can see that the vertex is located in x ≈ 70

The vertex of a quadratic equation is: x = -b/2a

so we have:

70 = -b/2a

let's try our options and see if we can discard other:

B:

-b/2a = 69.9/2 = 34.95

we can discard this option.

C:

-b/2a = 78/2 = 39 we can discard this option.

D:

-b/2a = 69.9/2*0.5 = 69.9

This is the only one that fits, so this is the correct option.

Answer:

Its D!!

Step-by-step explanation:

Answer:

In my own words interest rate is the  proportion of a loan that is charged as interest to the borower, typically expressed as an annual percentage of the loan outstanding. :D Hope this help and do you like brownies

Step-by-step explanation:

Final answer:

The interest rate is the cost of borrowing money or the return on investment deposited in financial institutions. It's influenced by financial regulations like usury laws, which cap the maximum interest rate to prevent excessive charges.

Explanation:

The interest rate is often referred to as the "price" of borrowing money in the financial market, and it's also the rate of return on an investment. When you deposit money into a savings account at a bank, the bank will pay you interest, which is a percentage of your deposits. This is the interest rate. Conversely, when you take out a loan, you will pay interest to the lender, which is the cost of borrowing the funds you need to purchase something, like a car or a computer.

There are also regulations like usury laws that set maximum limits on the interest rates that can be charged, ensuring that lenders do not exceed legal thresholds. The concept is similar to the idea of minimum wage, which sets a 'price floor' for hourly wages, below which it is illegal for employers to pay employees.

Answer:

If Hank shoots from inside the three-point line we can say that he has to shoot 246 inches to make the ball into the hoop.

Hank's distance from the center of the basket, if he is shooting from inside the three-point line, would be less than the distance of the three-point line from the basket. This distance varies between 6.75 metres (NBA, FIBA) or 6.1 metres (college games).

When a player stands inside the three-point line in basketball, it can be said that they are less than 6.75 metres (for NBA and FIBA) or 6.1 metres (for college games) from the centre of the basket. This distance varies because different basketball associations have different guidelines for the distance of the three-point line from the center of the basket. For instance, the NBA has its line located 7.24 metres from the basket, FIBA has it at 6.75 metres, and in college games, it's 6.1 metres away. As such, if Hank is shooting inside the three-point line, he is definitely standing closer than these distances to the basket's center.

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Answer:

2n+4

Step-by-step explanation:

To represent the number of turnips based on the number of radishes (n), the correct expression is 2n + 4, which means twice the number of radishes plus four.

The student is asking to write an expression for the number of turnips a rabbit eats, given that the number of turnips is four more than twice the number of radishes. If n represents the number of radishes, the expression for the number of turnips is 2n + 4.

Here's the step-by-step explanation:

Let n be the number of radishes.

According to the question, the number of turnips is twice the number of radishes, plus four. This is written mathematically as 2n (twice the number of radishes) plus 4 (four more).

So, the expression for computing the number of turnips is 2n + 4.

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Answer:

  0.4

Step-by-step explanation:

The conditions are mutually exclusive (X cannot be both 0 and 2), so the probability is the sum of the individual probabilities:

  P(x = 2 or 0) = P(x=2) +P(x=0)

  P(x = 2 or 0) = 0.1 +0.3

  P(x = 2 or 0) = 0.4

Answer:Probability of the tie going well [tex]=\frac{2}{3}[/tex]

Step-by-step explanation:

Given

There are 27 ties in closet out of which 18 go well with coat

and remaining 9 does not go well with coat

Probability of the tie going well [tex]=\frac{\text{Choosing a go well tie}}{\text{choosing a tie out of 27 }}[/tex]

Probability of the tie going well [tex]=\frac{18}{27}=\frac{2}{3}[/tex]

Probability of the tie not going well [tex]=\frac{\text{Choosing a not go well tie}}{\text{choosing a tie out of 27 }}[/tex]

Probability of the tie not going well [tex]=\frac{9}{27}=\frac{1}{3}[/tex]

Odds in favor of the tie going well is [tex]=18:9=2:1[/tex]

Odds against of the tie going well is [tex]=9:18=1:2[/tex]

The probability of picking a tie that matches the sport coat is 2/3 or .67, with the odds being 2:1. The probability of choosing a tie that does not match the sport coat is 1/3 or .33, with the odds being 1:2.

The topic at hand is about probability and odds. Probability defines the likelihood that an event will occur out of all possible outcomes, while odds compare the likelihood of the event happening to it not happening.

In this situation, Casey has 27 ties in total. The probability of him picking a tie that goes well with the sport coat is the number of favorable outcomes – 18 ties – over the total number of outcomes – 27 ties. So, the probability would be 18/27 which simplifies to 2/3 or approximately .67.

The odds of this happening, on the other hand, are 18 to 9 or simplified to 2:1. This means that for every three ties he picks, two are likely to go well with the sport coat.

The probability of picking a tie that doesn't go well with the sportcoat is 9/27, which simplifies to 1/3 or approximately .33. The odds of this are 9 to 18, or simplified to 1:2. This means that for every three ties he picks, one is likely not to match the sport coat.

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Answer:

45 is 5 times as many as 9 and 9 times as many as 5 :)

Step-by-step explanation:

45 is 5 times as many as 9 and is 9 times as many as 5.

We have the following statement -

45 is x times as many as 9 and is y times as many as 5

We have to find x and y.

n will be equal to -

n = ab

According to the question -

45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -

45 = [tex]x[/tex] x 9     ---(1)

and

45 = y x 5     ---(2)

Now -

Solving both, we get -

x = 5 and y = 9

Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.

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Answer:

there is equal probability for each outcome

Step-by-step explanation:

Let's say you are flipping a coin.

The possible outcomes are : Head and Tail

Probability(Head) = 1/2

Probability(Tail) = 1/2

In this case, there is equal theoretical probability of each outcome

Answer:

  -1, +3

Step-by-step explanation:

The equation can be factored as ...

  2(x² -2x -3) = 0

  2(x -3)(x +1) = 0

The zeros are the values of x that make the factors zero:

  x = 3, x = -1

The zeros are -1 and 3.

Answer:

1.5 hours per lawn

Step-by-step explanation:

Take the hours and divide by the number of lawns

9 hours / 6 lawns

1.5 hours per lawn

Answer:

See Explanation

Step-by-step explanation:

A prime number is a number that has only two factors, by 1 and itself.

A composite number on the other hand are numbers which have more than two factors.

To determine the number of prime cards needed to build each composite number, we first express the number as a product of its prime factors.

These are:

4=2X2

6=2X3

8=2X2X2

9=3X3

10=2X5

12=2X2X3

14=2X7

15=3X5

16=2X2X2X2

18=2X3X3

20=2X2X5

21=3X7

22=2X11

24=2X2X2X3

26=2X13

27=3X3X3

28=2X2X7

30=2X3X5

32=2X2X2X2X2

33=3X11

34=2X17

35=5X7

36=2X2X3X3

38=2X19

39=3X13

40=2X2X2X5

42=2X3X7

44=2X2X11

45=3X3X5

46=2X2X13

48=2X2X2X2X3

49=7X7

50=2X5X5

Therefore for each of the numbers, those are the prime number cards to be used.

Take for example, the number 50, the prime numbers that will be used to build 50 are the prime factors of 50.

50=2 X 5 X 5

Therefore, its prime factors are 2 and 5.

We will use the following prime number cards:

Answer:

so Area of Outer part = 8x + 16 square inches

Step-by-step explanation:

2 squares.

inner square dimension is  x inches by x inches.

width of outer region= 2inches.

We want the area of the border around the inner square.

so

Area of border = B  =  Area of Large - Area of Inner

B = (x+4)^2  - x^2

B = x^2 + 8x + 16 -  x^2

B = 8x + 16  square inches

so Area of Outer part = 8x + 16 square inches

To find the area of the outer part of the rug, we need to follow these steps:

1. Calculate the area of the entire square rug including the inner square.
2. Calculate the area of the inner square.
3. Subtract the area of the inner square from the area of the entire rug to find the area of the outer part.

The side length of the inner square is x inches.

Since the width of the outer region is 2 inches on all sides, this width will be added to each side of the inner square twice (once for each side of the corner) when calculating the side length of the entire rug. Thus, the entire side length of the rug will be x + 2 + 2 inches, which simplifies to x + 4 inches.

Now let's perform the calculations step-wise:

Step 1: Calculate the area of the entire square rug.
The formula for the area of a square is side length squared (A = side^2), so the area of the entire rug is (x + 4)^2 square inches.
 
Step 2: Calculate the area of the inner square.
Using the same formula (A = side^2), the area of the inner square is x^2 square inches.

Step 3: Subtract the area of the inner square from the area of the entire rug.
Now we subtract the area of the inner square from the area of the entire rug to find the area of the outer region:  
Area of the outer part = Area of the entire rug - Area of the inner square
Area of the outer part = (x + 4)^2 - x^2

To make it clearer, let's expand (x + 4)^2 using the distributive property (FOIL: First, Outer, Inner, Last):

(x + 4)^2 = (x + 4)(x + 4)
         = x*x + 4*x + 4*x + 4*4
         = x^2 + 4x + 4x + 16
         = x^2 + 8x + 16

So the Area of the outer part is:

Area of the outer part = x^2 + 8x + 16 - x^2
Area of the outer part = 8x + 16 square inches

This is the area of the outer part of the rug.

Answer:

0.078 or 7.8%

Step-by-step explanation:

Mean salary (μ) = $37,764

Standard deviation (σ) = $5,100

The z-score for any given teacher's salary in California, X, is determined by:

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

For X = $45,000:

[tex]z=\frac{45,000-37,764}{5,100}\\ z=1.419[/tex]

A z-score of 1.419 corresponds to the 92.20th percentile of a normal distribution. Therefore, the probability that a salary is greater than $45,000 is:

[tex]P(X>\$45,000) = 1-0.9220\\P(X>\$45,000) = 0.078=7.8\%[/tex]

The probability is 0.078 or 7.8%.

To find the probability of a teacher's salary being more than $45,000 in California, calculate the Z-score using the formula given and find the corresponding probability. This calculation reveals there's a 7.78% chance of a randomly selected teacher's salary exceeding $45,000.

To find the probability that a randomly selected teacher’s salary in California is greater than $45,000 when the salaries are normally distributed with a mean of $37,764 and a standard deviation of $5,100, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, X = $45,000, μ = $37,764, and σ = $5,100.

Calculating the Z-score gives us: Z = ($45,000 - $37,764) / $5,100 ≈ 1.42. Using the Z-table or a calculator with normal distribution functions, we find that the area to the right of Z = 1.42 corresponds to the probability we are looking for.

This area represents the probability that a teacher’s salary is greater than $45,000. Since we know the total area under the normal curve equals 1 (or 100%), the area to the right of Z = 1.42 is approximately 0.0778, which means there is a 7.78% chance that a randomly selected teacher’s salary in California is greater than $45,000.

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C cannot be folded upon any axis and lay upon itself.

Answer:

The area of trapezium is 87.5 cm square.

Step-by-step explanation:

Calculate are of trapezium by:

Base 1 (10cm)+ Base 2 (15cm) divided by 2 and times height (7cm)

Please mark brainiest

Answer:

x=4

Step-by-step explanation:

The solution for the logarithmic equation is x = 4 and it is graphically shown in the figure.

Every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation.

For the given situation,

The equation is

[tex]log_{2}x+log_{2}(x-2) =3[/tex]

⇒ [tex]log_{2} (x)(x-2)=3[/tex]

⇒ [tex]log_{2}(x^{2} -2x)=3[/tex]

we know that [tex]y=log_{b} x[/tex] can be written as [tex]x=b^{y}[/tex]

⇒ [tex]x^{2} -2x=2^{3}[/tex]

⇒ [tex]x^{2} -2x-8=0[/tex]

⇒ [tex](x-4)(x+2)[/tex]

⇒ [tex]x=4[/tex] or [tex]x=-2[/tex]

The solution for the logarithmic function is shown in the graph below.

Hence we can conclude that the solution for the logarithmic function is x = 4.

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Answer:

largeness

Step-by-step explanation:

look up in dictionary

Answer:

8 x 17 x 15 = 2040 that's your area

Step-by-step explanation:

good day and be safe

∵∴∵∴∵∴∵∴∵      

⊕ΘΞΠΤ⊕      

∵∴∵∴∵∴∵∴∵

Answer:

60 units squared

Step-by-step explanation:

The formula for the area of the triangle is: [tex]\frac{base*height}{2}[/tex]

To work this out you would first have to multiply 8 by 15, which gives 120. Then you would divide 120 by 2, Which gives you 60. This is because the formula is the same for the area of a square however the triangle is half of a square that has the same dimensions.

1) Multiply 8 by 15.

[tex]8*15=120[/tex]

2) Divide 120 by 2.

[tex]120/2=60^{2}[/tex]

The expressions 1.62 ÷ 0.8, 16.2 ÷ 8, and 0.0162 ÷ 0.008 all have the same value of 2.025, while 0.08 ÷ 0.08 has a different value of 1.

To solve this problem, calculate each of the expressions:

So, the first three expressions are the same because they all equal 2.025. However, the fourth expression is different because it equals 1. In the given question, they are not all equal. Thus, the values of three expressions could be 2.025, and the value of the fourth expression could be 1.

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Answer:

The experimental probability  of the coin landing on tails is 1/3

Step-by-step explanation:

Total no. of times coin tossed = 18

No. of times lands on head = 12

No. of times lands on tail = 18-12

No. of times lands on tail = 6

We are supposed to find  the experimental probability  of the coin landing on tails

So,  the experimental probability  of the coin landing on tails =[tex]\frac{\text{favorable outcome}}{\text{Total outcome}}[/tex]

So,  the experimental probability  of the coin landing on tails =[tex]\frac{6}{18}[/tex]

So,  the experimental probability  of the coin landing on tails =[tex]\frac{1}{3}[/tex]

Hence the experimental probability  of the coin landing on tails is 1/3

Answer:

The price of tomato per pound is $1.36

Step-by-step explanation:

Jordan has $5.37.

He is buying one red pepper for $1.29

He is also buying three pounds of tomatoes.

If he has exactly the right amount of money he needs, then

5.37 = 1.29 + 3x

Where x is the price of tomato per pound

And( 5.37 = 1.29 + 3x) is the equation to solve for x

5.37 = 1.29 + 3x

5.37-1.29 = 3x

4.08 = 3x

4.08/3 = x

1.36 = x

The price of tomato per pound is $1.36

To verify it again..

3*1.36 + 1.29

= 4.08 +1.29

= 5.37 ( which is the initial total amount)

Answer:

Jordan has $5.37, which he is using to buy ingredients to make salsa. He is buying one red pepper for $1.29 and three pounds of tomatoes. If Jordan has exactly the right amount of money he needs, what is the price per pound of the tomatoes?

Choose the correct equation to represent this real-world problem.

✔ 5.37 = 3x + 1.29

Solve the equation and verify the reasonableness of your answer.

A pound of tomatoes costs

✔ $1.36

.

Step-by-step explanation: