Find the value of the function sin 12pi/7
a. 3.11
c. –0.78
b. 0.99
d. 0

Pre-Calculus A-CR Circular Functions Practice UNIT 5: TRIANGLES IN CIRCLES: Circular Functions

Pierre has £102 and Alex has £62.

Let's assume that Pierre has x pounds and Alex has y pounds.

According to the given information:

If Pierre gave Alex £20, they would have the same amount: x - 20 = y + 20

If Alex gave Pierre £22, then Pierre would have twice as much as Alex: x + 22 = 2(y - 22)

We can solve this system of equations to find the values of x and y.

From equation 1), we can rewrite it as x - y = 40.

Substituting this value into equation 2), we get x + 22 = 2((x - 40) - 22).

Simplifying the equation, we have x + 22 = 2x - 124.

Bringing all the x terms to one side and the constant terms to the other side, we have 124 - 22 = 2x - x.

Simplifying further, we get 102 = x.

Substituting the value of x back into equation 1), we have 102 - y = 40.

Solving for y, we get y = 102 - 40 = 62.

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The length of the arc that corresponds to the angle is 6 cm.

Given in the question-

θ = 2 radians

r = 3 cm

We know that the formula to calculate the length of the arc is,

L = r * θ

where,

L is the length of the arc

r is the radius

θ is the central angle in radians

Putting values into the formula we have,

L = 3 * 2

  = 6 cm

∴ The length of the arc that corresponds to the angle is 6 cm.

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Answer:

The standard form of the given equation is y(x) = 2x² - 12x + 9.

Step-by-step explanation:

To rewrite the equation y(x) = 2(x-3)² - 9 in standard form, we need to expand the square term (x-3)², simplify the expression, and arrange the terms in descending order of degree.

First, we can expand the square term using the formula (a-b)² = a² - 2ab + b². In this case, a = x and b = 3, so we have:

[tex]\begin{aligned}\sf:\implies (x-3)^2& =\sf x^2 - 2(3)x + 3^2\\& =\sf x^2 - 6x + 9\end{aligned}[/tex]

Substituting this expression into the original equation, we get:

[tex]\sf:\implies y(x) = 2(x^2 - 6x + 9) - 9[/tex]

Next, we can simplify the expression by distributing the 2:

[tex]\sf:\implies y(x) = 2x^2 - 12x + 18 - 9[/tex]

[tex]\sf:\implies y(x) = 2x^2 - 12x + 9[/tex]

Finally, we can rearrange the terms in descending order of degree (highest power of x first):

[tex]\sf:\implies y(x) = 2x^2 - 12x + 9[/tex]

Therefore, the standard form of the given equation is y(x) = 2x² - 12x + 9.

Greetings! ZenZebra at your service, hope it helps! <33

Answer:

A

Step-by-step explanation:

5/18 = 0.2777 = 0.27° so when you divided thd no. it is 0.277777 and 7 is repeat .

Answer:

12 Hotdogs & 10 Hamburgers

Step-by-step explanation:

H - Hamburgers ; D - Hot Dogs

First make two equations :

H+D=22 ; since we sold 22 of both in total

4H+2D=64 ; since the total amount of money raised was $64

Now, use elimination to solve

-4(H+D=22) ; multiplying the first equation by -4 so that the H cancels out

-4H-4D=-88 + 4H+2D=64

4H   +2D      =64

-4H    -4D      =-88

-2D=-24

D=12

Then substitute D into an equation

H+12=22

H=10

Checking

4(10)+2(12)=64

40+24=64

64=64

So, the yearbook club sold 12 hot dogs and 10 hamburgers

10 Hamburgers

12 Hot Dogs

The ways I showed are not the only ways you could do this, the most important parts are getting the right equations and checking your work

Answer:

Set your calculator to degree mode.

[tex] \cos(x) = \frac{3.9}{8.5} [/tex]

[tex]x = {cos}^{ - 1} \frac{39}{85} = 62.7 \: degrees[/tex]

Angle x measures 62.7°.

Answer:

62.7

Step-by-step explanation:

For angle x, 3.9 is the adjacent leg.

8.5 is the hypotenuse.

cos Θ = adj/hyp

cos x = 3.9/8.5

cos x = 0.4588235

x = cos^-1 0.4588235

x = 62.68878

Answer: 62.7

The probability of obtaining the observed results or more extreme results under the assumption of the null hypothesis.

The P value is a statistical measure that helps to determine the level of significance of a hypothesis test. In hypothesis testing, the null hypothesis is the initial assumption that is tested against an alternative hypothesis.

The decision criterion for a hypothesis test using the P value is to compare the calculated P value with the specified significance level, denoted by alpha (α).
If the calculated P value is less than or equal to the specified significance level, we reject the null hypothesis.

This means that we have sufficient evidence to support the alternative hypothesis, which is the opposite of the null hypothesis.

The significance level is typically set at 0.05 or 0.01, which means that we are willing to accept a 5% or 1% chance of making a type I error (rejecting the null hypothesis when it is actually true).
It simply means that we do not have enough evidence to reject it at the specified significance level.
In conclusion,

The decision criterion for a hypothesis test using the P value is straightforward.

If the P value is less than or equal to the specified significance level, we reject the null hypothesis.

Otherwise, we do not reject the null hypothesis.

This decision is based on the level of evidence that is provided by the calculated P value.

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The simplified expression is sin(π).

To simplify the expression sin(3π/14) + sin(π/5) + sin(2π/7) + sin(3π/10), we cannot directly factor out the sin term like you mentioned. However, we can simplify the expression by finding common denominators for the angles and then combining like terms.

To begin, let's find a common denominator for the angles:

The denominators for the given angles are 14, 5, 7, and 10. The least common multiple (LCM) of these denominators is 70.

Now, let's rewrite each angle with a denominator of 70:

sin(3π/14) = sin(15π/70)

sin(π/5) = sin(14π/70)

sin(2π/7) = sin(20π/70)

sin(3π/10) = sin(21π/70)

Now we have:

sin(15π/70) + sin(14π/70) + sin(20π/70) + sin(21π/70)

Since the denominators are now the same, we can combine the terms:

sin(15π/70) + sin(14π/70) + sin(20π/70) + sin(21π/70) = sin[(15π + 14π + 20π + 21π)/70]

Simplifying the numerator:

15π + 14π + 20π + 21π = 70π

Plugging it back into the expression:

sin[(15π + 14π + 20π + 21π)/70] = sin(70π/70) = sin(π)

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The distance that the tip of the minute hand travels to go from 1 :27 to 1 : 43 would be 13.4 inches.

First, find the angle from 1 :27 to 1 : 43 :

From 1:27 to 1:43, there are (43 - 27) = 16 minutes which means the angle is:

Angle = 16 minutes × 6° /minute = 96°

The distance can be found by using the arc length formula :

= Radius × Angle (in radians)

= 8 inches ×  ( 96° ×  ( 1 radian / 57. 3 °) )

=  8 inches × 1. 675 radians

= 13. 4 inches

In conclusion, the tip of the minute hand travels 13.4 inches.

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Answer:

118.3

Step-by-step explanation:

1.3 times 9 = 130% times 9 divided by 100 = 118.3

The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied.

The product of two irrational numbers can be rational or irrational.

For example, consider √2 and √2/2. Both are irrational numbers, as they cannot be expressed as a ratio of two integers.

Their product is:

√2 × √2/2 = √2 × √2 × 1/2 = 2/2 = 1

which is a rational number.

On the other hand, consider √2 and √3.

Both are irrational numbers. Their product is:

√2 × √3 = √6

An irrational number.

A pair of irrational numbers might have a logical or irrational result.

For instance, think about 2 and 2/2. Since neither can be expressed as a ratio of two integers, they are both irrational numbers. However, their product is a rational number

Consider, however, options 2 and 3. Both numbers are irrational. Their output is

an unreasonable quantity.

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The relevant long-run proportion of interest and use it to make predictions or draw conclusions about the population as a whole.

The relevant long-run proportion of interest refers to the proportion or probability of an event occurring over a large number of trials or in the long run.

It is the proportion or probability that we would expect to observe if we were to repeat the same experiment or process a large number of times under similar conditions.

For example,

If we are interested in the proportion of defective products produced by a manufacturing process.

The relevant long-run proportion of interest would be the proportion of defective products that we would expect to observe if we were to produce a large number of products using the same manufacturing process.

This proportion can be used to assess the quality and effectiveness of the manufacturing process and to make decisions about how to improve it.

Similarly,

In statistical inference, we often use the relevant long-run proportion of interest to make inferences about the population parameter based on a sample.

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Answer:

x= 4 1/3

Step-by-step explanation:

3x-4=9

3x=13

x=13/3 = 4 1/3

Answer:

4 and 1/3

Step-by-step explanation:

Move -4 to the # side of the equation and change the symbol:

3x=9+4

Solve:

3x=13

x=13/3

x=4 and 1/3

The parent function of this equation is 2ˣ,domain of the given function is all real numbers, ange of the given function is y < -3, the y-intercept is -7 and  horizontal asymptote is y = -3.

The given function is y = -((2)ˣ⁺² - 3

The parent function of this equation is 2ˣ.

The domain of the given function is all real numbers since  2ˣ is defined for all x.

The range of the given function is y < -3 since the exponential function  2ˣ always produces positive values, and when we add a negative constant and subtract another constant, we shift the range downwards.

The y-intercept of the function is found by setting x = 0:

y = -((2)² - 3 = -7

So the y-intercept is -7, which means the function intersects the y-axis at the point (0, -7).

The horizontal asymptote is y = -3.

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The difference in the elevation between Los Angeles and Death Valley is 48 feet.

Given that,

Maria drove from Los Angeles to Death Valley.

Elevation of Los Angeles = 330 feet

Elevation of Death Valley = 282 feet

We have to find the difference in elevation between Los Angeles to Death Valley.

Difference in elevation between Los Angeles to Death Valley is,

Difference = 330 feet - 282 feet

                  = 48 feet

Hence the difference is 48 feet.

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Yes, that is correct. To determine a 99% confidence interval using the interval of plausible values method, we need to use a significance level of 0.01 on the two-sided tests.

This is because a 99% confidence interval means we want to be 99% confident that the true population parameter (e.g. mean or proportion) falls within our calculated interval. This corresponds to a significance level of 0.01 (1-0.99) for a two-sided test.

In other words, we want to find the interval of plausible values that includes the sample statistic (e.g. sample mean or proportion) with a probability of 0.99, while rejecting values outside that interval with a probability of 0.01 split between the two tails of the distribution.

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To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, we cannot consult the regression [tex]R^2[/tex]  because the [tex]R^2[/tex] values for these models are not directly comparable.

This is because the[tex]R^2[/tex] values are calculated differently for linear and logarithmic models.

In a linear model,[tex]R^2[/tex] measures the proportion of the variance in the dependent variable (Yi) explained by the independent variable (X).

In a logarithmic model, [tex]R^2[/tex] measures the proportion of variance in the natural log of the dependent variable (ln(Yi)) explained by the independent variable (X).

Since the dependent variables are different in both models, comparing [tex]R^2[/tex] values would not provide a meaningful measure of how well each model fits the data.

Instead, we should consider using other methods to compare the two models, such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC), which account for model complexity and goodness-of-fit.

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The value of P(A U B) is 0.6352 if P(A) = 0.24 and P(B) = 0.52 when A and B are independent.

In the question, P(A) and P(B) denote the Probability of events A and B happening.

Given that, P(A) = 0.24 and P(B) = 0.52

Now, we have to find the value of P(A∪B).

P(A∪B) = P(A) + P(B) - P(A)*P(B)

P(A)*P(B) = 0.24×0.52

P(A)*P(B) = 0.1248

Now, P(A∪B) = P(A) + P(B) - P(A)*P(B)

P(A∪B) = 0.24 + 0.52 - 0.1248.

P(A∪B) = 0.76 - 0.1248

P(A∪B) = 0.6352.

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The amount paid back when the loan is paid in full at the end of that period will be $77,546.3.

Given that:

Principal, P = $35,000

Rate, r = 7.5% or 0.075

Time, n = 11 years

The amount (A) is calculated as,

A = P(1 + r)ⁿ

If the loan is paid in full at the end of that period, then the amount paid back is calculated as,

A = $35,000 x (1 + 0.075)¹¹

A = $35,000 x (1.075)¹¹

A = $35,000 x 2.2156

A = $77,546.3

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The solution is, it hailed for 1 hour long.

Here, we have,

given that,

It started hailing at 10:30 A. M.

The hail stopped at 11:30 A. M.

now, we have to find that How long did it hail.

so, we have to get the difference in time of starting and ending.

we have,

The hail stopped at 11:30 A. M.

and, It started hailing at 10:30 A. M.

so, the difference in time = long it hailed

we get,

11:30 A. M.  - 10:30 A. M.

=11:30 -10:30

=1 hour.

Hence, The solution is, it hailed for 1 hour long.

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The  answer to the multiple choice question is that a t distribution has slightly broader tails than the Z distribution. This is because the t distribution is based on smaller sample sizes and therefore has more variability, leading to wider tails.

Additionally, the explanation for the other options is as follows:
- A t distribution can be positively or negatively skewed depending on the sample size and distribution of the data.
- A t distribution does have a nonzero mean, just like any other distribution.
- As mentioned earlier, a t distribution has slightly broader tails than the Z distribution.
- A t distribution does have asymptotic tails, meaning they approach but never reach zero as the degrees of freedom increase.

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An equation relating G to D is G = 14 - D/35.

A graph of the equation using the axes is shown in the image below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about Rav's trip on the highway, we have the following slope and y-intercept;

Slope, m = -1/35.

y-intercept, c = 14.

By substituting the given parameters, we have the following:

y = mx + c

G = Dx + c

G = -D/35 + 14

G = 14 - D/35

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The area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Since kite ABCD is divided into two triangles by its diagonals, we can find the area of the kite by finding the sum of the areas of these two triangles.

Let AC and BD be the diagonals of the kite, intersecting at point E. Then triangle ABE and triangle CDE are the two triangles formed by the diagonals.

The area of a triangle can be found using the formula: Area = (base x height) / 2

For triangle ABE, the base is AB and the height is the distance from E to the line containing AB. Similarly, for triangle CDE, the base is CD and the height is the distance from E to the line containing CD.

Since the diagonals of a kite are perpendicular and bisect each other, the distance from E to the line containing AB is the same as the distance from E to the line containing CD.

Therefore, the heights of the two triangles are equal.

So, we can find the area of ABCD as follows:

Area of ABCD = Area of triangle ABE + Area of triangle CDE

= (AB x height)/2 + (CD x height)/2

= (AB + CD) x height / 2

Therefore, the area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

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The value of the expression which is twice the sum of a number and eight, increased by three squared” when n=4 would be = 33

Let the unknown number be represented as n = 4

From the statement above,

Twice the sum of a number (4) and 8.

That is;

= 2(4+8)+ 3²

= 2(12)+ 9

= 24+9

= 33

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Step-by-step explanation:

Given:-

The average person drinks 16 ounces of milk a day.

Find:-

how many gallons will a person drink in a year?

We know that,

Leap years have = 366 days.

8 pints in per gallon.

So,

366/8

45.75

The survey designers can help ensure that they are getting accurate and representative responses from their participants.

The way questions are worded or the order in which they are asked can significantly impact people's responses and ultimately influence the accuracy of the survey results. Here are two specific ways in which this can happen:
1. Question Wording Effect: This refers to the impact of the specific wording of the survey questions on people's responses.

This effect is especially pronounced for questions that are complex, sensitive, or controversial.
2. Question Order Effect: This refers to the impact of the order in which the survey questions are presented on people's responses.

Similarly, if a survey question asks about a person's level of satisfaction with a product before asking about their experience with the product, it may influence their overall satisfaction rating.
Overall,

It is important to carefully consider the wording and order of questions when designing a survey to ensure accurate and reliable results.

By avoiding biased or leading questions and carefully considering the order in which questions are presented.

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Answer:

We have shown that any integer that can be represented as the sum of squares of two rational numbers can also be represented as the sum of squares of two integers.

Step-by-step explanation:

Let the integer be represented as $n=a^2+b^2$ where $a,b \in \mathbb{Q}$.

Let $a=\frac{p}{q}$ and $b=\frac{r}{s}$ such that $p,q,r,s$ are integers with no common factor.

Then, $nq^2s^2=p^2s^2+q^2r^2$.

Since $p^2s^2$ and $q^2r^2$ are perfect squares, their sum is also a perfect square.

Let $nq^2s^2=x^2$. Then, $(p^2s^2+x^2)=(q^2s^2)^2$.

This shows that $q^2s^2$ must divide $p^2s^2+x^2$, and hence $q^2s^2$ is a perfect square.

Let $q^2s^2=y^2$. Then, $y \in \mathbb{Z}$ and $(aqs)^2+(bys)^2=n(y^2)$.

Thus, We have shown that any integer that can be represented as the sum of squares of two rational numbers can also be represented as the sum of squares of two integers.

Approximately 8.73 pounds of chamomile tea should be mixed with 12 pounds of orange tea to make a mixture that costs $14.88 per pound.

Let's assume x represents the number of pounds of chamomile tea that needs to be mixed.

The cost of chamomile tea per pound is $18.40, and the cost of orange tea per pound is $12.24. We want to find the quantity of chamomile tea that, when mixed with the given 12 pounds of orange tea, will result in a mixture costing $14.88 per pound.

The total cost of chamomile tea in the mixture is given by 18.40x dollars, and the total cost of orange tea is 12.24 * 12 = 146.88 dollars.

The total cost of the mixture is the sum of the costs of chamomile and orange tea, which is 14.88 * (x + 12) dollars.

Since the total cost of the mixture is equal to the sum of the costs of the individual teas, we can set up the equation:

18.40x + 146.88 = 14.88 * (x + 12)

Now, let's solve for x:

18.40x + 146.88 = 14.88x + 177.6

Subtracting 14.88x from both sides:

3.52x + 146.88 = 177.6

Subtracting 146.88 from both sides:

3.52x = 30.72

Dividing both sides by 3.52:

x = 30.72 / 3.52

x ≈ 8.72727

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