Using trig to find a side.
Solve for x. Round to the nearest tenth, if necessary.

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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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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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

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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In the circle the mesaure of ∠ACF is  7

The distance from the centre of a circle to any point on the boundary is called the radius. The radius is half of the diameter; 2r=d 2 r = d . The line segment that joins two points on the circle is a chord.

If diameter of a circle bisects a chord ,then it must be perpendicular to the chord.

∴ m∠ACF = 90°  

(8x + 34)° = 90°

8x = 90 - 34

x = 56/8

x = 7

Hence,mesaure of ∠ACF = 7

Complete question : In Circle C, the diameter AB bisects the chord EF.

If m∠ACF = (8x+34)°, enter in the correct value of x.

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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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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 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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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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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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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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this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.

A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.

Here are the steps for conducting a repeated measures ANOVA:

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Answer: False

Step-by-step explanation:

1/7 x 1/7 = 1/49 x 1/7 = 1/343

The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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Answer:

31.4 cm

Step-by-step explanation:

Circumference of circle = D x π

D = 10 cm

π = 3.14

Let's solve

10 x 3.14 = 31.4 cm

So, the circumference of the circle is 31.4 cm

The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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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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Answer:

use desmos graphing calculator it helps alot

Step-by-step explanation:

x^{2}-x-6=0 has two zeros/solutions

x^{2}-x-6=0 has 1 zero/solution

x^{2}-x-6=0 has no zero/solution

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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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)

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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All the possible angle measures are given as follows:

25º and 35º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

On the first quadrant, we have that:

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Answer: 32

Step-by-step explanation:

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

The money Jodi will have after selling her shares will be B. $5160.00

What is meant by selling?

Selling typically refers to the exchange of goods or assets for money or other valuable consideration. It is the process of transferring ownership of a product or item from the seller to the buyer in return for an agreed-upon price or value.

What is meant by shares?

Shares refer to units of ownership in a company or corporation. When a company sells shares, it is raising funds from investors who then become shareholders and have a claim on the company's profits and assets.

According to the given information

Jody bought 20 shares of Amazon at $121.00, which costs her 20 x $121.00 = $2420.00.

One year later, she bought 20 more shares at $127.00, which costs her 20 x $127.00 = $2540.00.

The total cost of buying all the shares is $2420.00 + $2540.00 = $4960.00.

Jody sold all her shares two years later at $133.00 per share, which gives her 40 x $133.00 = $5320.00.

Her total profit is $5320.00 - $4960.00 = $360.00.

After deducting the broker's fees, Jody will have $360.00 - $80.00 = $280.00.

Therefore, the correct answer is option B. $5160.00.

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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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Answer:

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

The given dimensions are:

Length = 9 yd

Width = Pyd (it's unclear what this means, so let's assume it's a typo and the intended value is 3 yd or 4 yd)

Height = 4 yd

Assuming the width is 3 yd, the volume of the rectangular prism is:

Volume = Length x Width x Height

Volume = 9 yd x 3 yd x 4 yd

Volume = 108 cubic yards

Assuming the width is 4 yd, the volume of the rectangular prism is

Volume = Length x Width x Height

Volume = 9 yd x 4 yd x 4 yd

Volume = 144 cubic yards

Therefore, the volume of the rectangular prism is either 108 cubic yards or 144 cubic yards, depending on the intended value of the width.

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

Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

The rate of return on the account was 11.429% over the course of 15 years.

Interest rate is the percentage charged by a lender to a borrower for the use of money. It is the cost of borrowing money, expressed as a percentage of the amount borrowed. Interest rates are typically determined by the prevailing market conditions, the type of loan product being offered, the borrower's credit score, and the lender's risk tolerance. The higher the interest rate, the more expensive the loan will be for the borrower.

The rate at which the account earned interest can be calculated using the following formula:

Rate = (Interest Earned/Principal) * (1/Number of Years)

In this case, the rate is:

Rate = (2000/3500) * (1/15)

Rate = 0.11429 or 11.429%

This means that the account earned 11.429% in interest over the course of 15 years. This rate of return is relatively modest, as interest rates are often much higher than this. In fact, the current average rate of return for a 15-year CD is around 1.75%.

The reason why the rate of return is so low is likely due to the fact that the account was earning interest at a fixed rate. Fixed rate accounts typically offer lower interest rates than variable rate accounts, since the bank or financial institution is making a guarantee that the rate will not change. This makes them less risky for the investor, but also less profitable.

In conclusion, the rate of return on the account was 11.429% over the course of 15 years.

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