1. two six-sided, fair dice are rolled. what are the probabilities of getting one even and one odd number?

The probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69.

Since a person with type B blood can safely receive blood transfusions of type O and type B blood, the fourth donation selected at random must be either type O or type B blood. From the information given, the probability of the fourth donation being type O blood is 49%, and the probability of it being type B blood is 20%. Therefore, the probability that the fourth donation can be safely used in a blood transfusion on someone with type B blood is:

P(type O or type B) = P(type O) + P(type B) = 0.49 + 0.20 = 0.69

So, the probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69 (rounded to the nearest thousandth).

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we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11

9, 1, 6

First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To divide 5,472 by a two-digit number, we can use long division method as follows:

34) 5 4 7 2( 34

   -    4 0

     ______

       1 4 7

  -    1 3 6

      _______

            1 1

Therefore, we get the quotient as 161 and remainder as 11.

So the missing numbers are:

R = 11

9, 1, 6

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The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

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The upper control limit for the p-chart is 0.111, and the lower control limit is 0.003.

To calculate the upper and lower control limits for a p-chart, we need to use the following formula:

UCL = p' + 3√(p'(1-p')/n)

LCL = p' - 3√(p'(1-p')/n)

Where p' is the mean proportion of defective pots, n is the sample size (in this case, 120), and UCL and LCL are the upper and lower control limits, respectively.

Given that the proportion of defective pots is believed to be 0.05, we can calculate the mean proportion of defective pots as:

p' = 0.05

Substituting this value in the above formula, we get:

UCL = 0.05 + 3√(0.05(1-0.05)/120) = 0.111

LCL = 0.05 - 3√(0.05(1-0.05)/120) = 0.003

Any sample proportion of defective pots falling outside these limits would be considered statistically significant and warrant further investigation to identify the root cause of the defects in the production process.

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Complete question is:

A random sample of 120 cast aluminum pots is taken from a production line once every day. the number of defective pots is counted. the proportion of defective pots has been closely examined in the past and is believed to be 0.05. what are the upper and lower control limits for the p' chart.

Expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72.[/tex]

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity. It can consist of constants, variables, arithmetic operators, and other mathematical functions or operations.

The expression [tex]162x^2 - 72[/tex] can be factored using the difference of squares formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex].

First, we can factor out 18 from the expression:

[tex]162x^2 - 72 = 18(9x^2 - 4)[/tex]

Now, we can apply the difference of squares formula by setting a = 3x and b = 2:

[tex]9x^2 - 4 = (3x)^2 - 2^2 = (3x + 2)(3x - 2)[/tex]

Substituting this back into the original expression, we get:

[tex]162x^2 - 72 = 18(9x^2 - 4) = 18(3x + 2)(3x - 2)[/tex]

Therefore, expressions (i) and (v) are equivalent to the original expression [tex]162x^2 - 72[/tex].

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A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

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The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

Answer:

15

Step-by-step explanation:

The numbers in the given data = 12, 17, 16, 10, 20

Total number = 5

12 + 17 + 16 + 10 + 20 = 75

Mean = 75/5

Mean 15

The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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Answer:

25

Step-by-step explanation:

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

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The two statements are;

The area of sector 1 is  20n² + 15n square meters

The total distance around the garden is 20n + 2 meters

Option A  and C

The formula for the area of a rectangle is expressed as;

A = lw

Such that the parameters are;

For the first sector, we have that;

Length = 4n + 3

Width = 6n - 2 - 5n = n - 2

Substitute the values

Area of sector 1 = (4n + 3)(5n)

expand the expression

Area of sector 1 = 20n² + 15n square meters

Area for the sector 2

Area = (3n - 3)(n -2)

expand the bracket

Area = 3n² - 6n - 3n + 6 = 3n² - 9n + 6

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Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

Yes , it is appropriate to choose normal approximation to calculate the chance of winning at least 10 times out of 75 total plays of game.

Use the normal approximation,

Chance of winning at least 10 times out of 75 total plays of the game,

Conditions for using the normal distribution are met.

Binomial distribution can be approximated by the normal distribution,

The number of trials 'n' is large enough usually n > 30.

The probability of success 'p' is not too close to 0 or 1.

The trials are independent.

Here,

n = 75 trials and p = 0.15 probability of winning.

To check if the normal approximation is appropriate,

Calculate the mean and standard deviation of the binomial distribution,

mean = n × p

         = 75 × 0.15

         = 11.25

Standard deviation

= √(n × p × (1 - p))

= √(75 × 0.15 × 0.85)

= 3.09

Mean is 11.25 and the standard deviation is 2.44.

The condition for independence is satisfied since each play is independent of the others.

If the other two conditions are met,

Check if np and n(1-p) are both greater than or equal to 10,

np = 75 × 0.15

    = 11.25

n(1-p) = 75 × 0.85

         = 63.75

Both np and n(1-p) are greater than or equal to 10,

So the conditions for using the normal approximation are satisfied.

Therefore, it is appropriate to use the normal approximation to find the chance of winning at least 10 times out of 75 total plays of the game.

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The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

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Therefore, while these results do suggest that there may be a difference in SAT Critical Reading scores between students who learned English and another language simultaneously and the general population, further research is needed to understand the extent and causes of this difference.

Based on the information provided, it seems that students who learned English and another language simultaneously score lower on the SAT Critical Reading exam than the general population of test takers. The mean score of the general population is 501, while the mean score of the sample of 100 test takers who learned English and another language simultaneously is 485. This is a difference of 16 points, which could be considered statistically significant.

However, it is important to note that the standard deviation of the sample is quite high at 116. This suggests that there is a lot of variability in the scores of students who learned English and another language simultaneously, which could be due to a variety of factors such as differences in language proficiency or educational background.

Therefore, while these results do suggest that there may be a difference in SAT Critical Reading scores between students who learned English and another language simultaneously and the general population, further research is needed to understand the extent and causes of this difference.

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The results do not provide sufficient evidence to suggest that students who learn English and another language simultaneously score worse on the SAT critical reading exam than the general population of test takers.

We will use the terms: mean, standard deviation, sample size, and hypothesis testing.
Mean score among all test takers: 501
Mean score of the bilingual students' sample: 485
Standard deviation of the bilingual students' sample: 116
Sample size: 100.
To determine if bilingual students score worse on the SAT critical reading exam, we will conduct a hypothesis test.
Formulate the hypotheses
Null hypothesis (H0):

Bilingual students' mean score = General population mean score
Alternative hypothesis (H1):

Bilingual students' mean score < General population mean score
Calculate the test statistic
Test statistic = (Sample mean - Population mean) / (Standard deviation / sqrt(Sample size))
Test statistic = (485 - 501) / (116 / sqrt(100))
Test statistic = -16 / 11.6
Test statistic ≈ -1.38
Determine the critical value and significance level
We'll use a one-tailed test with a significance level (α) of 0.05. Using a standard normal (Z) table, the critical value is -1.645.
Compare test statistic to critical value
Since our test statistic (-1.38) is greater than the critical value (-1.645), we fail to reject the null hypothesis.

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Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

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Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

The granite countertop would cost $783.00.

Finding the cost of granite:

To find the cost of granite find the amount of granite that can be used for the entire kitchen.  

Since the kitchen floor is in a rectangle shape find the area of the kitchen floor using the area of a rectangle. Which will equal the amount of granite used for the kitchen.  

Use the formula for the cost of the countertop, which is the product of the area, and the cost per square meter, to determine the total cost.

Here we have

A counter in Adriana's kitchen is 1 m wide and 3 m long.

Hence, the area of the countertop can be found by multiplying the length and the width:

Area of kitchen = length x width = 3 m x 1 m = 3 m²

The cost of the granite is given by $ 261.00 per square meter

The cost of the granite countertop will equal the product of the area and the cost per square meter:

Total Cost = 3 m² x $261.00/m² = $783.00

Therefore,

The granite countertop would cost $783.00.

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a. The probability that the current component has been in operation for at least 50 hours is 0.5

b. The probability that the current component will last for at least 50 more hours is also 0.5.

(a) The probability that the current component has been in operation for at least 50 hours is given by the cumulative distribution function (CDF) of the uniform distribution on [100, 200] evaluated at 50.

The CDF of a uniform distribution on [a, b] is given by:

F(x) = (x - a) / (b - a) for a <= x <= b

F(x) = 0 for x < a

F(x) = 1 for x > b

Therefore, in this case, the CDF is:

F(x) = (x - 100) / 100 for 100 <= x <= 200

F(x) = 0 for x < 100

F(x) = 1 for x > 200

So the probability that the current component has been in operation for at least 50 hours is:

P(ti >= 50) = 1 - F(50) = 1 - ((50 - 100) / 100) = 0.5

(b) The probability that the current component will last for at least 50 more hours is also given by the CDF of the uniform distribution on [100, 200], but evaluated at 150 instead of 50.

That is,

P(ti >= 150) = F(150) = (150 - 100) / 100 = 0.5.

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Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.

When we multiply all the common prime factors, we get the greatest common factor of the numbers.

These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.

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Answer: A

Explanation:

His discount and final price be $280 for his order of 140 boxes.

A discount is a drop in a product's or service's price.

It is frequently provided as a perk to customers to entice them to buy. Discounts are often stated as a percentage or dollar amount off the list price.

Depending on the sort of discount and the situation, discounts can be computed in a variety of ways.

For instance, a product that costs $100 would have a discounted price of $80 with a 20% discount applied. Similar to this, a product that costs $50 would have a discounted price of $40 if it received a $10 reduction.

In marketing and sales, discounts are frequently used to draw customers and boost sales volume.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test.

In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."

This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Exampe of Percentage :-

10% = 10/100 ( = 1/10 (or) 0.1)

25% = 25/100 ( = 1/4 (or) 0.25)

According to question

Lee qualifies for a 20% discount because his order of 140 boxes falls within the range of 100-200 boxes.

Since each box originally cost $2.50, the full price of 140 boxes, after any discounts, is:

140 * $2.50 = $350

The 20% Lee discount is determined as follows:

20% * $350 = $70

Lee's discount is therefore $70, and his adjusted price is as follows:

$350 - $70 = $280

Therefore, Lee will ultimately pay $280 for his order of 140 cartons.

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Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.

Any function which it graphs as a straight line is said to be linear. Mathematically speaking, this indicates that the function contains one or two variables, but neither exponents nor powers.

Given linear function:

y = 2x - 3 ; with x = 4

To get the value of y ,put x = 4 in the given function:

y = 2(4) - 3

y = 8 - 3

y = 5

Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.

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correct question:

Find the value of y for the given value of 'x'.

y = 2x - 3 ; x = 4

Answer: 32

Step-by-step explanation:

50% of last year is divided by 2 (50/100 = 1/2). 64/2 = 32

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

The inequality graphed is given as follows:

y ≥ x² - 4x - 5.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The roots of the parabola are given as follows:

x = -1 and x = 5.

Hence:

y = a(x + 1)(x - 5)

y = a(x² - 4x - 5).

When x = 0, y = -5, hence the leading coefficient a is given as follows:

-5a = -5

a = 1.

The part above is painted, with a solid line, hence the inequality is given as follows:

y ≥ x² - 4x - 5.

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Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

Let x be the number of cups of lemonade Jane sold.

The total earnings she made from selling x cups of lemonade is:

Total earnings = price per cup * number of cups sold

Total earnings = $0.25 * x

The total cost of making x cups of lemonade is:

Total cost = cost per cup * number of cups sold

Total cost = $1.50 * x

Jane's profit is equal to her total earnings minus her total cost:

Profit = Total earnings - Total cost

Profit = $0.25x - $1.50x

Profit = -$1.25x

We know that Jane's earnings were $9.75, so we can set up the equation:

$9.75 = -$1.25x

To solve for x, we can divide both sides by -$1.25:

-$9.75 / -$1.25 = x

x = 7.8

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

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The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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