The interior angle of a regular polygon IS 180°.find the value if its exterior regular polygon

Answer:

its a 1/6 chance

Step-by-step explanation:

each face has a 1/6 chance of being rolled since there are 6 faces

\(\\ \sf\longmapsto |11-x|=1\)

As we can see

\(\\ \sf\longmapsto D_f=\[1,11\]\)

So having 1 and 11 as domain we can say the equation is

\(\\ \sf\longmapsto |11-x|\geqslant 1\)

The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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We require 16 lbs of $2.95 coffee and 28 lbs of $3.30 coffee to produce 44 pounds of blended coffee.

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions, unique response, No remedy, and there are several options.

Let the coffee worth 2.95 pound = x.

Let the coffee worth 3.50 pound = y

The blend of 3.30 pound for 44 pounds is = 145.2.

Given that, coffee worth 2.95 a pound was mixed with coffee worth 3.50 a pound to produce a blend worth 3.30 a pound.

2.95x + 3.50y = 145.2.......(1)

We need to produce 44 pounds of coffee.

x + y = 44...........(2)

The equation 2 can be written as:

y = 44 - x

Substitute the value of y in equation 1:

2.95x + 3.50(44 - x) = 145.2

2.95x + 15.4 - 3.50x = 145.2

6.45x = 145.2 - 15.4

x = 16

Substitute the value of x in equation 2:

16 + y = 44

y = 28

Hence, we require 16 lbs of $2.95 coffee and 28 lbs of $3.30 coffee to produce 44 pounds of blended coffee.

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Answer:

-3 + 8 = 5

Step-by-step explanation:

When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.

LMK if you have questions.

-3 + -8 = -11

is that a nice one or something

Answer:

I think it would be A.....

The confidence limits for the proportion of voters planning to vote for the Democratic incumbent are approximately 0.558 and 0.662.

We have,

To find the confidence limits for the proportion of voters planning to vote for the Democratic incumbent, we can use the formula for a confidence interval for a proportion.

Given:

Sample size (n) = 500

Number of respondents voting for the Democratic incumbent (x) = 305

Confidence level (1 - α) = 0.99

First, we calculate the sample proportion (p-hat):

p-hat = x / n = 305 / 500 = 0.61

Next, we calculate the standard error (SE) of the proportion:

SE = √((p-hat x (1 - p-hat)) / n)

= √((0.61 x (1 - 0.61)) / 500)

= 0.020

Using the z-score corresponding to a 0.99 confidence level, which is approximately 2.576, we can calculate the margin of error (ME):

ME = z x SE = 2.576 x 0.020 = 0.052

Finally, we can calculate the confidence interval:

Confidence Interval = p-hat ± ME

Confidence Interval = 0.61 ± 0.052

Therefore,

The confidence limits for the proportion of voters planning to vote for the Democratic incumbent are approximately 0.558 and 0.662.

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Answer

7% . .                                  ...................                              

Answer:

f

Step-by-step explanation:

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

I understand that you would like an explanation related to parallel lines in geometry and the final answer should be concise, covering the main point in the last two lines.
In geometry, parallel lines are lines in a plane that never intersect or touch each other at any point. These lines always maintain the same distance from one another. However, if two lines start as parallel but later diverge, it indicates that they are no longer maintaining the same distance from each other. In such a case, the geometry under consideration is non-Euclidean.

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

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Using linear approximation, the value of f(3.01) can be approximated by evaluating the tangent line to the function f(x) = x^2 at x = 3 and using it to estimate the value at x = 3.01.

Linear approximation is a method used to estimate the value of a function near a specific point by considering the tangent line at that point. The tangent line is a linear function that approximates the behavior of the original function in the vicinity of the point.

To approximate f(3.01) using linear approximation, we start by finding the slope of the tangent line at x = 3. This can be done by taking the derivative of f(x) = x^2, which is f'(x) = 2x. Evaluating f'(3) gives us the slope of the tangent line at x = 3.

Next, we use the point-slope form of a linear equation to write the equation of the tangent line. Plugging in the values x = 3, y = f(3) = 9, and the slope from f'(3), we can determine the equation of the tangent line.

Finally, we evaluate the tangent line at x = 3.01 to approximate the value of f(3.01). This can be done by substituting x = 3.01 into the equation of the tangent line and solving for y. The resulting value is an approximation of f(3.01) using linear approximation.  

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Answer:

x-intercept: (2,0)

y-intercept: This line doesn't cross the y-axis.

Step-by-step explanation:

\(\sf \leadsto \dfrac{5y - 2}{4(y + 2)} = \dfrac{1}{3}\)

\(\sf \leadsto \dfrac{5y - 2}{4y + 8} = \dfrac{1}{3}\)

\(\sf \leadsto 3(5y - 2) = 1(4y + 8)\)

\(\sf \leadsto 15y - 6 = 4y + 8\)

\(\sf \leadsto 15y - 4y = 8 + 6\)

\(\sf \leadsto 11y = 14\)

\(\sf \leadsto y = \dfrac{14}{11}\)

Answer:y=14/11

Step-by-step explanation:

Answer:

The statement is False

Explanation:

Statement: Two triangles that have congruent angles are congruent.

The statement is False.

As a counterexample, consider the two triangles below:

The two triangles above have congruent angles 45°-45°-90.°

However, the side lengths are not the same, thus, the triangles are not congruent, hence supporting our claim that the given statement is False.

\(11x-21=8x+15\\3x-21=15\\3x=36\\x=\boxed{12}\)

\(LM=11(12)-21=\boxed{111}\\\\MN=LM=\boxed{111}\\\\LN=111+111=\boxed{222}\)

Answer:

x=7

Step-by-step explanation:

5x-6=3x+8

subtract 3x from both sides

2x-6=8

add 6 to both sides

2x=14

divide both sides by 2

x=7

Answer:

\( -40s + 90t + 30 \)

Step-by-step explanation:

Given, \( -10(4s - 9t - 3) \)

To clear parenthesis using the distributive property of multiplication, we have,

\( -10(4s) -10(-9t) -10(-3) \)

Negative sign multiplied by negative sign = positive sign

\( = -40s + 90t + 30 \)

Thus:

\( -10(4s - 9t - 3) = -40s + 90t + 30 \)

The given series is: $\sum_{n=1}^\infty\frac{7(-1)^n}{n^n}$To find whether the given series is convergent or divergent we can use the ratio test.Suppose: $a_n=\frac{7(-1)^n}{n^n}$Then, $a_{n+1}=\frac{7(-1)^{n+1}}{(n+1)^{n+1}}$So, $\lim_{n\to\infty} \frac{a_{n+1}}{a_n}=\lim_{n\to\infty} \frac{7(-1)^{n+1}}{(n+1)^{n+1}}\cdot\frac{n^n}{7(-1)^n}$$\

Rightarrow \lim_{n\to\infty} \frac{(-1)^{n+1}}{(-1)^n}\cdot\frac{n^n}{(n+1)^{n+1}}=\lim_{n\to\infty} \frac{n^n}{(n+1)^{n+1}}$Now, we can take the natural logarithm of both the numerator and denominator of the limit, so that we can use L'Hopital's rule.\begin{align*}\lim_{n\to\infty} \ln\left(\frac{n^n}{(n+1)^{n+1}}\right)&=\lim_{n\to\infty} \ln n^n-\ln(n+1)^{n+1}\\&=\lim_{n\to\infty} n\ln n-(n+1t(\frac{n^n}{e^n}\cdot\frac{e^{n+1}}{(n+1)^{n+1}}\right)\right]\\&=\lim_{n\to\infty} \ln\left(\

frac{n}{n+1}\right)^{n+1}\\&=-\lim_{n\to\infty} \ln\left(\frac{n+1}{n}\right)^{n+1}\\&=-\lim_{n\to\infty} (n+1)\ln\left(1+\frac{1}{n}\right)\\&=-\lim_{n\to\infty} \frac{\ln\left(1+\frac{1}{n}\right)}{\frac{1}{n+1}}\cdot\frac{n+1}{n}\\&=-1\end{align*}Thus, $\lim_{n\to\infty} \frac{a_{n+1}}{a_n}=e^{-1}=\frac{1}{e}$Therefore, the series is absolutely convergent as $\frac{1}{e}<1$Hence, the given series is convergent.

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Answer:

76 is the correct one. So you surely go for it

180-106=74

180= 74 + 30 + x

180 - 104 = x

76 = x

Therefore B) 76 is the answer

Answer:

A

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

To the nearest year, $5,000 invested at 5% per year, compounded daily, will be worth $10,000 in approximately 14 years.

To determine the time it takes for the investment to double, we can use the compound interest formula: A = P(1 + r/n)^(n*t), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $5,000, the annual interest rate (r) is 5% (or 0.05), and the investment is compounded daily, so the number of times interest is compounded per year (n) is 365. We want to find the number of years (t) it takes for the investment to reach $10,000.

Setting up the equation: 10,000 = 5,000(1 + 0.05/365)^(365*t), we can solve for t using logarithms or trial and error. The result is approximately 14 years. Therefore, it will take approximately 14 years for the $5,000 investment to grow to $10,000 at a 5% annual interest rate, compounded daily.

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Answer:

A

Step-by-step explanation:

The saying "government who governs less governs best" is accurate, therefore yes.

Given that,

What does the statement from paragraph 12 that "the government that rules the least, governs the best" mean, in your opinion? Which of the following statements, based on your knowledge of history, is true.

According to the aforementioned claim, governments that strive to have less bureaucratic and autocratic control over the country prefer to give their inhabitants more freedom and civil rights.

Therefore, in order to keep peace, the government should not interfere too much in social and economic affairs through restrictive laws and regulations unless it is absolutely required for the good of the country.

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The correct statement that describes Type I and Type II errors in hypothesis testing is:

b. Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error occurs when the null hypothesis is accepted when it is actually false.

In hypothesis testing, Type I error refers to rejecting the null hypothesis when it is actually true. This error represents a false positive result, indicating that a significant effect or relationship is detected when it does not exist in reality. Type II error, on the other hand, occurs when the null hypothesis is accepted (not rejected) when it is actually false. This error represents a false negative result, indicating a failure to detect a significant effect or relationship that does exist. The correct understanding and interpretation of Type I and Type II errors are crucial in hypothesis testing to ensure accurate conclusions.

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The height of the flagpole is 27 feet.

Given,

If two triangles are similar, sides of these triangles will be proportional.

Height of the flagpole  = h feet

Shadow castes by the flagpole  = 72 feet

Height of the person  = 6 feet

Shadow casted by the person = 16 feet

By using the property of similar triangles,

Hence, h/6 = 72/16

h = (6×72)/ 16

h = 27 feet

Therefore, The height of the flagpole is 27 feet.

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Answer:

VT = 37.8 ft

Step-by-step explanation:

Here, we want to get the measure of VT

We need the diagram of the triangle here

We can get this in the attachment

From the diagram, we have it that the hypotenuse is the length UT since it faces the right angle

VT does not face the given angle , nor the right angle; this mean VT is the adjacent

Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine

Thus;

cos 66 = VT/UT

cos 66 = VT/93

VT = 93 * cos 66

VT = 37.83

To the nearest tenth of a foot, VT = 37.8 ft

a. The test at the 5% significance level indicates no significant difference in the incidence rate of GI problems between those who consume olestra chips and the TG control treatment. b.  To detect a difference between the true percentages of 15% and 20% with a probability of 0.90, a sample size of 29 individuals is necessary for each treatment group (m = n).

How to carry out hypothesis test?

To carry out the hypothesis test, we can use a two-sample proportion test. Let p₁ represent the proportion of individuals experiencing adverse GI events in the TG control group, and let p₂ represent the proportion in the olestra treatment group.

Null hypothesis (H₀): p₁ = p₂

Alternative hypothesis (H₁): p₁ ≠ p₂ (indicating a difference)

Given the data, we have:

n₁ = 529 (sample size of TG control group)

n₂ = 563 (sample size of olestra treatment group)

x₁ = 0.176 x 529 ≈ 93.304 (number of adverse events in TG control group)

x₂ = 0.158 x 563 ≈ 89.054 (number of adverse events in olestra treatment group)

The test statistic is calculated as:

z = (p₁ - p₂) / √((\(\hat{p}\)(1-\(\hat{p}\)) / n₁) + (\(\hat{p}\)(1-\(\hat{p}\)) / n₂))

where \(\hat{p}\) = (x₁ + x₂) / (n₁ + n₂)

b. We want to determine the sample size (m = n) necessary to detect a difference between the true percentages of 15% and 20% with a probability of 0.90.

Step 1: Define the given values:

p₁ = 0.15 (true proportion for the TG control treatment)

p₂ = 0.20 (true proportion for the olestra treatment)

Z₁-β = 1.28 (critical value corresponding to a power of 0.90)

Z₁-α/₂ = 1.96 (critical value corresponding to a significance level of 0.05)

Step 2: Substitute the values into the formula for sample size:

n = (Z₁-β + Z₁-α/₂)² * ((p₁ * (1 - p₁) / m) + (p₂ * (1 - p₂) / n)) / (p₁ - p₂)²

Step 3: Simplify the formula since m = n:

n = (Z₁-β + Z₁-α/₂)² * ((p₁ * (1 - p₁) + p₂ * (1 - p₂)) / n) / (p₁ - p₂)²

Step 4: Substitute the given values into the formula:

n = (1.28 + 1.96)² * ((0.15 * 0.85 + 0.20 * 0.80) / n) / (0.15 - 0.20)²

Step 5: Simplify the equation:

n = 3.24² * (0.1275 / n) / 0.0025

Step 6: Multiply and divide to isolate n:

n² = 3.24² * 0.1275 / 0.0025

Step 7: Solve for n by taking the square root:

n = √((3.24² * 0.1275) / 0.0025)

Step 8: Calculate the value of n using a calculator or by hand:

n ≈ √829.584

Step 9: Round the value of n to the nearest whole number since sample sizes must be integers:

n ≈ 28.8 ≈ 29

The complete question is:

Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms. Among 529 individuals in the TG control group, 17.6% experienced an adverse GI event, whereas among the 563 individuals in the olestra treatment group, 15.8% experienced such an event.

a. Carry out a test of hypotheses at the 5% significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment.

b. If the true percentages for the two treatments were 15% and 20% respectively, what sample sizes (m = n) would be necessary to detect such a difference with probability 0.90?

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The measurement of ∠STU is 20°.

Define Angle

When two rays are connected at their endpoints, they form an angle in geometry. We refer to these rays as the angle's sides or arms.

Components of an Angle

An angle is composed of the arms and the vertex as its two basic components:

Given, ∠STU = \((\frac {1}{4} x+8)\)°

∠UTV = x+2°

Given, that the line TV bisects ∠STU,

∠STV = ∠UTV

Substitute their values,

\((\frac {1}{4} x+8)\)° = x+2°

Calculating,

\(\frac{1}{4}x-x\) = 2-8

\(-\frac{3}{4}x\) = -6

x = \(-6*(-\frac{4}{3})\)

x = 8

So, we know that:

∠STU = ∠STV + ∠UTV

          =  \((\frac {1}{4} x+8)\)° +( x+2°)

          =  \((\frac {5}{4} x+10)\)

Now, substitute the value of x,

∠STU =  \((\frac {5}{4} )*8\)°+10°

          = 10° + 10°

          = 20°

Therefore, the measure of ∠STU is 20°.

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